Minecraft – play the Minecraft Classic Levels in Minecraft Beta

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.

Yes, you can do this.

First, download McEdit. Open up your Classic .lvl and save it, in McEdit, as a schematic. Then, make a super-flat world and open it (or create a new one with McEdit), and paste the schematic where you need it to be. Save it as a Minecraft world.

(Remember that you may need to patch things up; I did this once and I had to seal things up because lava was coming in, and the floor could reach the void.)