Does Lance still inflict piercing damage?

No, the Lance does not deal piercing damage in Monster Hunter World.

I picked Behemoth to test this, because of how different his hitzones are for the various types of damage. Behemoth's front legs have 50 and 40 hitzone values for sever and blunt respectively. His hind legs, on the other hand, have 30 and 55 hitzone values for sever and blunt.

If the Lance did piercing damage, it would deal more damage to Behemoth's hind legs than his front legs. Instead, the third upthrust dealt 57 damage on a crit to Behemoth's front legs, and 34 damage on a crit to Behemoth's hind legs. These numbers are consistent with the sever hitzone values, and the blunt hitzone values are completely ignored.