Could a creature be made entirely, or mostly of magma or lava? Could it sustainably live in or near a volcano for an extended period of time? Rocks around the outside are optional, and encouraged. If this cannot be achieved naturally, then that is sad.
By any scientific definition, the answer to your question is an emphatic NO.
Magma/Lava on the other hand are many times hotter. Reaching 5 - 10 times the temp of the hottest places life as we know it manages.
Your only option in this situation is magic.
Scientifically, not a chance. Silicate life, if it exist, might live in extremely hot environments due to various quirks of their supposed biochemistry, but it's still really sketchy. If you want to bring magic into the equation then sure, anything goes. But it sort of defeats the point of the question.
From my understanding of the life sciences multi cellular life requires well defined pockets for cells to do their work in, that's well defined in space, time, temperature, salinity, ph, and anything else involved in structure or metabolism.
So, if there's some measure of stability to be found in or around magma, sure there can be life.
Now, in extreme environments some very interesting adaptations have evolved such as super tough shields for snails near sulfur vents and antifreeze in the antarctic. But nothing we know of can retain its structure at magma temperatures.
So, if there's a way to protect its guts there can be life (as we know it) in or around magma.
Near the surface there's the problem of magma only existing for a short time. And the nature of magma is such that it melts everything as in material is reduced to atomic form and molecular bonds cannot form for long (not sure what you're going to make life out of other than molecules).
The most abundant elements in life are: oxygen, carbon, hydrogen, nitrogen, calcium and phosphorus. The melting point of calcium is 1548F, magma is about 2606F. Find some way to have proteins survive that temp and you've got life. Then again when pressure is higher so is melting temperature. So, you'd have a greater chance of life deeper in the planet.
However, you could have a creature's life cycle include magma somehow, maybe as spores. Something that didn't need to move around on its own. Why? Because anything that wants to move requires flexible parts and no matter how awesome and insulating your armor is it's going to need flexible parts with different mechanical properties for what its protecting to move around.
Maybe that can give you some hope.
Here's one idea that might have legs. You could possibly play out the concept of a being that can "thrive" in lava, but is perhaps not made of it. Maybe through tough exterior skin or shell the being can swim or live inside lava and use the immense heat and pressure to create energy through exchange and thus would "feed" off lava in a sense and almost need to be near it at all time like a fish in water as that's how it's body had adapted and grown.
From here you could play with the idea that the character has to wear some kind of "lava" suit outside of it's home like a astronaut needs to when walking and interacting outside it's environment. This suit could then appear to be flowing lava sustained inside shields or magic or what have you giving the character the appearance of a lava being.