Contrary to cinematic opinion, you don't sink:
Golem, if you remember, dove into the lava of Mt. Doom after his previous ring was thrown in – he proceeds to sink into the lava and leaves the ring floating on the lava until it melts away. Guess what? Sinking into lava just will not happen if you’re a human (or remotely human). You’d need to be a Terminator to sink into molten rock/metal … and here’s why. Molten lava is nothing like water.