A little while ago I posted this homebrew Patron option here. I got some great feedback and have returned not only with an update but also with some homebrew Invocations that support the overall Planescape theme I've been longing for in my games.

The Lady of Pain Patron

You have quietly made a Pact with the Lady of Pain and her Cage. As a shadow of Her Serenity, you have been charged with maintaining balance among the planes while preserving the Lady’s privacy. As part of this pact, you have the following restrictions & benefits:

• You must never divulge the nature of your pact, even under pain of
  death.


• You must protect the Dabu and the city of Sigil, and never bring
  either harm.


• Alcohol and other intoxicants have no diminishing effect on the pain
  you feel. Conversely, your tolerance for pain has increased by twice
  that of most mortal creatures.


• The City of Doors is intuitive for you to navigate; most doors there
  are available for your travel if they are not being actively
  obstructed or hidden.


• You can understand the strange visual language of the Dabu, but
  cannot communicate using it.

Expanded Spell List

1st: shield, inflict Wounds

2nd: cloud of daggers, heat metal

3rd: blink, glyph of warding

4th: greater invisibility, death ward

5th: planar binding, dispel evil and good

Features

Serenity’s Shadow

Starting at 1st level, you can as an action cast an ominous shadow in a 10-foot radius that provides you with several benefits:

• You gain a bonus to your AC equal to half your Charisma modifier,
  rounded down (minimum of +1).


• As part of a single melee attack, you can turn the shadow against
  hostile creatures, rendering them vulnerable to slashing,
  bludgeoning, and piercing damage for the attack. Once the shadow is
  used in this way, it recedes until you have taken a long rest.


• You can as an action while your shadow is active, gain advantage on
  Dexterity (Stealth) Checks. Once the shadow is used in this way, it
  recedes until you have taken a long rest.

At 10th level, the shadow’s aura protects and hides allies with its radius, which also expands to 30 feet. Additionally the powers of the shadow can be used a number of time equal to your Charisma Modifier (Minimum of 2) before needing to take a long rest.

Severance

By 6th level, your body has adapted to recovering from gruesome injuries. If you have hit points equal to or less than half of your hit point maximum, you can use an action to spend one hit dice + your Charisma modifier to regain hit points.

Planar Doorman

At 14th level, you can cast the plane shift spell once without using a spell slot or material components so long as you are headed to Sigil. You can use this feature to travel elsewhere if you possess the material component as normal. You can also immediately identify the plane and general location of someone is who is using a spell or magical effect to travel to another plane assuming they are within your visible range. As an reaction to the plane shift spell being cast by another creature, you can counter that spell immediately.
Using the feature in either of these ways will require a long rest before using either functionality again.

New Eldritch Invocations

The Lady's Maze

Prerequisites: Level 18, Lady of Pain Patron

You gain mastery of the specific pocket dimensions wherein the Lady of Pain stuffs Berks who displease her. You can cast the maze spell once without using a spell slot. The maze appears to be a circular series of platforms, paths, and portals.
The maze can also be cast on willing group of creatures equal to your Charisma modifier. items and inanimate objects left in the maze will remain there. If the maze is used in this way, you must succeed a DC 20 Intelligence check to end the spell early.
Once this Invocation has been used for either function you must take a long rest to gain access to the maze again.

Berk’s Bane

Prerequisites: Level 5, Lady of Pain Patron

You are becoming crueler to your foes as you now critical hit on an attack roll of 19 or 20 while your Serenity's Shadow feature is active, additionally you become proficient in the Intimidation Skill if you are not already.

Tormentor

Prerequisites: Level 10, Lady of Pain Patron, Pact of the Blade

Once per turn, you can deal an extra 3d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use your Pact Weapon. This invocation does not stack with the Rogue’s Sneak Attack Feature.

I thought you were a deader for sure!

Prerequisites: Level 12, Lady of Pain Patron

Injuries are a daily
occurrence in your line of work granting you further insight into
anatomy and medicine. You gain proficiency in the medicine skill,
additionally when you use the Severance feature you can reattach a
severed limb by holding a severed body part (other than your head) to
where it fell off. Once you use this feature to reattach a limb, you
can't use it again until you finish a long rest.

I like the concept a lot! I definitely don't think it's overpowered -- it might be underpowered, but not excessively so, in my opinion.

I think the main issue with this class (which I mention several times in the below points) is that its most powerful feature is Serenity's Shadow which it gets at 1st level. This has 2 issues: it encourages other classes to take a 1 level dip in this class, rather than sticking with it, and it makes later levels kind of boring, since you don't gain as much from later levels. I'd try to spread the power of Serenity's Shadow over multiple levels and I provide a few suggestions for that below:

• 
  

  Serenity's Shadow:

  
  
  
  
  
  1. You should specify that the radius is centered on yourself.
  
  
  2. Can any creature be made Vulnerable, even if they'd otherwise be immune?
  
  
  3. How long does the advantage on Stealth last? Since DMs often use one check to cover an extended period of stealth, is it ok if the advantage lasts a long time, or it it meant to only apply for the short period before the shadow retracts?
  
  
  4. I worry that the Vulnerability feature is a bit weak, since it only applies to a single attack and then reduces your AC for the entire day. @BlakeSteel points out that increasing its duration could be overpowered if other characters coordinate their actions to exploit it, but I see little issue with allowing it to apply to all of your attacks this turn (if you have Extra Attack, Thirsting Blade, Haste, or Two-Weapon Fighting or another form of Bonus Action attack).
  
  
  5. The main concern with this would be that it makes a 1-level dip extremely powerful. Moving that feature to a higher level would solve that problem, and give a nice boost to higher levels for a class that gets most of its best features at 1. So, at 1st level, it would only apply to a single attack, while at Level 10, it could apply to all attacks on your turn.
  
  
  6. If you're worried that the change in 4) is too powerful, you could make it kick in only at a higher level, and/or make it shift Vulnerability by one category: so Normal -> Vulnerable, Resistant -> Normal, or Immune -> Resistant
  
  
  7. To make this feature a bit clearer, I'd tie the number of uses to casting the shadow, then list the benefits while the shadow is out, and then list the actions that can be taken which use up the shadow. This way, you don't have the phrase "Once the shadow is used in this way, it recedes until you have taken a long rest", which becomes invalidated once you get multiple uses at 10th level.
  
  
  
  


• 
  

  Serenity's Shadow - AC Bonus:

  
  
  
  
  
  1. Since the AC bonus is worded as a flat bonus to AC, it would stack with the Monk's WIS bonus to AC, the Barbarian's CON bonus to AC, or the AC bonus from Mage Armor. Is this intended? If not, you should mimic the wording of those features and describe it as an alternate way to calculate base AC.
  
  
  2. I don't think letting the AC bonus stack is overpowered, but my main worry is that, since the feature is gained at Level 1, it would encourage 1 level dips, just to get the AC bonus. It's really flavorful, and I like getting it at 1st level, but you should find some way to make it scale with level to discourage 1 level dips
  
  
  3. Here's one suggestion for scaling: Let the shadow only be active for a limited number of turns per use (perhaps 1 + Warlock level). So, a 1 level dip would give you a free AC bonus for only 1 or 2 turns per day; good, but not overpowered. At level 5, it's probably safe to make it last indefinitely, since that's a significant investment.
  
  
  
  


• 
  

  Severance:

  
  
  
  
  
  • Is it meant to have unlimited uses (assuming you have hit dice remaining)?
  
  
  • The wording on this is unclear. I'd reword it to mimic the Durable feat:
    
    

    
    

    "you can use an action to roll one Hit Die to regain hit points, the amount of hit points regained is equal to the die roll plus your Charisma modifier"

    
    

    
    
  
  
  
  


• 
  

  Planar Doorman:

  
  
  
  
  
  1. The section that states: "You can also immediately identify the plane ..." I assume this refers to the location they're going to plane shift to, right? That's unclear from the wording.
  
  
  2. The first clause should mimic the invocations that add spells: "You can cast plane shift once using a warlock spell slot. You can’t do so again until you finish a long rest. If you are traveling to Sigil, this does not use a spell slot or material components".
  
  
  3. Does the reaction to counter plane shift also use up the free planeshift? Does it prevent you from tracking people who try to plane shift?
  
  
  4. I think it would be cool if, instead of just countering the casting of plane shift, you also had the option to use plane shift to follow that person.
  
  
  
  


• 
  

  I thought you were a deader for sure!:

  
  
  
  
  
  • Does this ability only apply to yourself?
  
  
  • This ability is pretty underpowered, since most DMs don't give their PCs crippling injuries. I'd expand the healing potential by giving you the change to cast Regenerate as a Warlock spell once per day, perhaps with the side effect of it being excruciatingly painful.
  
  
  
  


• 
  Restrictions and Benefits:
  
  
  
  
  • As Miniman points out, the ability to navigate the City of Doors listed "Restrictions and Benefits" look like fluff or a roleplaying hook, but could actually be extremely mechanically powerful, especially if the campaign takes place in Sigil.
  
  
  • No other patrons have mechanical benefits in their description - if you want this to be a specific power that Lady of Pain Warlocks have, you should make it a class feature, perhaps part of Planar Doorman
    
  
  
  • A better option, in my opinion, would be to remove any explicit powers of navigation and, instead, state that the Lady of Pain can, at her discretion or in exchange for a deal/favor, grant this power to assist players in carrying out her will. This puts control of the feature in the DM's hands and reduces the odds that you'll disrupt the campaign by intuitively navigating to the BBEG's secret lair.
  
  
  
  

Tormentor is not a problem to stack with a Rogue's sneak attack.

Here is why.

You have to spend 10 Warlock levels to get that invocation, which is 10 levels of rogue that you can't have.

At level 10, rogues get 5d6 on sneak attack. Compare:

• Rogue at 20 has 10d6 sneak attack bonus damage.



• 
  

  Rogue 10/Warlock 10 has 8d6 sneak attack (equivalent) damage.

  
  
  

  DPR numbers: Going from 1.05 X 8d6 (29.4) to 1.10 x 8d6 (30.8) with the increased crit chance (19, 20 using Berk's Bane) does not overtake pure Rogue for sneak attack of 1.05 X 10d6 (36.75).

  
  
  

  Your choice to limit to "once per turn" is sufficient brake on exploits.

  
  
  

  Recommendation: let it stack.

  
  

Severance seems underpowered for a level six ability.

(Compare to Shadow Sorcerer's Hound feature, for example ...)

Recommendation: Revise Severance's heal to a bonus action, or a reaction. It's a modest healing for during combat, and can only get you (at best) back to half HP.

Serenity's Shadow: obscure, dim light, darkness ... what is it?

You need to clarify that a bit so that we know how it interacts with light and various forms of vision (dark vision, devil's sight, etc).

I think Severance is still to strong. Delete the "you can reattach a limb", and it will be good. The rest, is I think, good (even if I would have made Tormentor stack with Sneak attack)

edit: you've done it ^^