Can you fish in Lava?

Actually, as Johonn and Finn Rayment suggested in the comments above, lava does not interact properly with the fishing rod. It does not burn the lure, and it just (appears) to sink to the bottom of the lava pool, unlike when fishing in water, it will float.

It does not cause any damage to the rod at all, while casting onto dry land, or any other mob or entity will cause damage to the rod.

This was tested in 1.8.1, in both Survival and Creative, (there was no difference between the gamemodes) though I am unaware of the behaviour in earlier versions. It does seem bugged however, due to the odd behaviours I described above.