Summary:
Pillars of dripstone are generated on lava as if on stone. That is, they do not go into the lava, but end at the surface of the lava.

Seed and coordinates (1.18.0):

Seed: 1792249514
Coords: -1384 -14 -4553

Steps to reproduce:

1. Create a world with the above seed.
2. Visit the coordinates above.

Observed results:
Pillars of dripstone blocks end at the surface of the lava.

Expected results:
Pillars of dripstone blocks will go under the lava (rather than float on the lava).

Image: