Float your boat on lava?

Solution 1:

Boat float on lava? Yes

Sail the boat? No

The player may place boats in lava, but if they try to ride the boat it will break and they will fall into the lava.

A video of a boat placed on lava

Using a Splash Potion of Fire Resistance can cause boats to be immune to fire.
When riding a boat through lava without it dying, it will attach to the nearest block and will not be ridden like a boat on water.

Edit:

"(...)if you use a fishing rod to pull yourself forward then?" – Marco Geertsma

It doesn't work, the boat doesn't move if you use it, and it doesn't move on water with that technique either. And it would be annoying fishing with that.

Solution 2:

No, you are not. This is completely illogical... You can place the boats into lava but if you try and use it, you will fall into the lava and die horribly.

Read this for more information: http://www.minecraftwiki.net/wiki/Boat