Mojang forgot to make it so that mobs eventually drown in lava like in water. This includes players. Noticeable effects on gameplay are few, but it is still an oversight, as old as lava itself. It was forgivable back then because no mob could survive in lava long enough to be able to drown in it. I'd say that there were no noticeable effects on gameplay until they added Zombie Pigmen, which have intrinsic fire resistance. Even though you could drown one in water, which back then was only observable in vanilla if a pig got struck by lightning, you couldn't drown one in lava.

Minecraft 1.0 made it more noticeable when you were able to gain extrinsic fire resistance through a potion. When you drank it and swam in lava, there was no air meter. Logically the only time you should be able to breathe under lava is when you are under the effects of both fire resistance and water breathing, the latter of which isn't brewable yet but is functional.

If the water breathing effect is extended to apply to lava as well, it could be renamed simply "Breathing", or something to that effect which sounds cooler. It could possibly also extend to suffocation damage, so witches would drink it if someone attempted to build a suffocation trap with them.

This would probably also necessitate a new mob flag that gives a type of mob the intrinsic ability to breathe in lava, but not water. This would work well with Magma Cubes, and perhaps Blazes. Maybe Ghasts as well so they don't fly into a one-block thick lavafall and drown from that.