It will crumble if you hit it with a hammer, yes, but not just by being in a tank. How much is up to you, it depends how big the bits are, how much of the tanks you want to take up etc.
I may have read somewhere that lava rock is not good for inverts, i think it produces problems in moulting. Could be thinking of another type of rock, though if you have inverts it may be worth checking out .
I've kept lava rock with inverts and have no problem. I don't see how it can cause any problems with molting though. The LFS here sells them for 2 bucks for a pound of rock.
You should scrub it, since it tends to have lots of little loose bits.