When in a lake of lava deeper than two blocks you sink and get stuck at the bottom. You cant swim up and out.
The Lava disappears completely looking like normal view. You will be on fire but the screen will not be red.
I have included two images one looking at the pool. You'll notice a dirt block in the right side of the wall. The second is an image of me at the bottom of the lava pool. In front and above is the same dirt block.