In fact they already do, even without a fantasy element. There are any number of extremophiles that live in high temperature environments (which volcanoes tend to be). There are also extremophiles that live in highly acidic or basic environments. Then we've got some of the more exotic bacteria and plants that live in the dark and feed off volcanic vent activity at the bottom of the sea.
Now: Most of these tend to be simple lifeforms, and they all like having water around (though some of them don't seem to care if it's so acidic it can eat metal). Either your volcanoes get regularly rained on and the environment is very humid, you're next to the sea, or the volcanoes interact with a subterranean aquifer of some kind. Slimes and gels are the order of the day. Oh yeah..
Since you're in a fantasy environment we can expand the criteria a bit. Sentient, acidic slimes can be quite the hazard. Nests of burrowing worms that eat silicates aren't out of the question (and are horrible if they fall on your head). Plantlife (of a sort. Probably best not to try eat them) can exist, using heat to bind resources leached from the rocks using acid distilled from the vapours in the air. If you want to you can build a whole ecosystem based around hot, acidic creatures. They will suffer from hypothermia if you move them far from their natural habitat though, and though they might be able to eat us I doubt we'd have the right PH to make a tasty snack.
Unless you're willing to dive very deep into the realm of fantasy you can't have things living in the lava. While you might conceivably be able to handwave heat resistance into them, anything that sinks in lava is going to have to be denser than the molten rock it's living in, which means either your lava-dwellers actually float on the surface or they take years to sink/emerge, and they've got to be ungodly strong. While lava looks like it flows easily, it actually doesn't. It's still as dense as granite and has a tendency to freeze around cooler things that get put into it.
Bring on the Flaming Jesus Lizards.