That's a weird Larianism - Lolthsworn isn't a race in DnD. I get why Larian did it -- it's a weird consequence of Larian trying implement alignment while WotC is trying to ditch it.
But, yes, the drow can forswear Lolth and serve other gods. The drow are a bit different than other evil races - orcs, goblins and the like were created by their gods to serve them as slaves. The drow are a fallen, corrupted people.
