Lava Veins

There could be lava veins under some mountains implying that the mountain is a volcano that isn't active.

The lava veins could be made out of magma blocks and the deeper parts of the veins could be made out of lava. Maybe the magma blocks should start shading into lava at the Y-level 0 so that there wouldn't be too much lava. At the bottom of the vein there could be a cave filled with lava. Also the veins could start to form one big vein once it starts to reach the lava cave. The lava cave is always located at the bottom of the world.

How to fix some of the problems with this idea:

I think the generation of these veins should be quite rare so that there wont be too much lava on your way when you are mining.

The lava shouldn't be visible to air so that there wont be too much lava falls in the walls of caves. The lava source blocks that are visible to air should generate as magma blocks.