How can I get out of the lava without dying?

First of all, backup your world directory so you can try things over and over again. (Although you should remember that you might spent more time trying to rescue yourself than you'd need to get your stuff again)

Then set the difficulty to peaceful which slows your dying (but doesn't prevent it!). Now if you have some blocks in your inventory on a hotkey, after unpausing immediately look down, switch to the blocks and hold SPACE (jump) and hold right click. If you're lucky this is fast enough to build a tower out of the lava (which is hopefully not too deep). You'll still be burning, which doesn't kill you on peaceful, but if you have a bucket of water put that on the side of your tower to get a small waterfall which also obsidianizes the lava below. Good look!

Alternatively you can use a map tool to change the lava pool you're in into water, but that would really be cheating.

Grab yourself MCEdit, and change your character's location so they're not in the lava. For extra safety, place them in water to extinguish any residual flaming.

Change the difficulty to the easiest setting, this will let you regenerate health quicker and reduce the damage you take from the lava, if you're lucky then it may buy you just enough time to get clear of the lava.