Hcfyk

The dog lifted its hind leg towards the fire hydrant.

I am not sure I like using the preposition "towards" in this sentence. I prefer "on", because it sounds nice, but I am not sure if it's correct at all. Is it correct? Why?

I think an aspect of this that @Wilson is missing is that a dog "lifting its leg" is usually used as a euphemism for a male dog urinating [on something].

In my experience in this 'non literal' context, it takes the same preposition logically as 'urinate' would take.

The dog urinated on the fire hydrant.

The dog lifted his leg on the fire hydrant.

When I read the example "The dog lifted its hind leg onto the fire hydrant" it seemed very strange to me. It sounded like the dog literally lifted his leg and placed it on top of the hydrant.

"Lifted his leg towards" sounds like the dog is saluting the fire hydrant.

So, to me, as someone whose male dog spends a lot of time lifting his leg on things in my company, "to lift his leg on" is the most natural choice.

The dog lifted its hind leg towards the fire hydrant.

The leg is now nearer to the fire hydrant than before, or nearer than the other parts of the dog. This is what dogs usually do when they want to mark their territory by leaving their smells behind. Peeing in other words.

The dog lifted its hind leg onto the fire hydrant.

The leg is now resting on the fire hydrant, so that the dog is possibly standing with three legs on the pavement and one leg somehow on top of the fire hydrant. It's not what dogs usually do.

The dog lifted its hind leg on the fire hydrant

It's occurred to me that on has a markedly rarer meaning as a malefactive. Something like "He hung up on me!" means "he ended the phone call to my detriment, or against my will or interest". In that way, the dog lifting its leg on the fire hydrant sounds odd to me, but I'll accept it.

At is for places:

The dog lifted his hind leg at the fire hydrant or when he got to the fire hydrant.

On and in do not work here.

Dogs generally just aim at the hydrant. They aim at the fire hydrant and hit the side of it, not the top. So on is out. Unless you have a really big dog.

So lifted at can be understood as aiming and peeing. Or it can mean that is the place where he lifted his hind leg.

Like: We stopped at the house for a cup of tea. :)

OK:

The scientists found that when away from their home area, these dogs were more likely to urinate frequently and aim their urine at objects in comparison to when they were walked close to home. The authors concluded “urination in female dogs does not function solely in elimination, but that it also has a significant role in scent marking…”
peeing positions and what they mean, by vets

When they pee, the urine may fall on the object, nevertheless, they pee at an object like a fire hydrant or tree.

A non-native English speaker, I often have to rely solely on the usage examples from original English language pieces of literary work and dictionaries; so looking for examples, I came across

The dog lifted its leg against the lamp..

And here's the example of using the preposition on in the context of a male dog preparing to pee.

That said, I absolutely agree on using the preposition "on" and can't but agree on the preposition "at" suggested in the answer and approved of in the comment on it, both being provided by native English speakers. At the same time, the other suggestions are well worth being taken note of, as quite possible alternatives.

As a side note, "hind" seems to be redundant, logically, in such a situation (IMHO)