No, she did not, at least not the one true
Lolth, that of Greyhawk. I really don't like the FR Drow pantheon, never made sense to me, and I really hate the "it looks good, let's copy it, but way worse, in the FR" attitude.
As for what happens when a god is killed, I really liked the 4e Adventure Path "Scales of War", including the consequences of what happens if the goddess of Greed is killed, with the speech by Bahamut: "Good and evil alike are affected by the end of greed and envy—which you saw in Hestavar. Even bulwarks of virtue like the temple of Bahamut are not immune to greed.” Bahamut gives a low snort that might be a chuckle,
might be a cough. “There’s still evil in the world, of course. The tree of evil has multiple roots . . . not just greed. But you’ve fundamentally changed the world forever, heroes. I encourage you to visit it and see what you’ve done before . . . moving on."
Some of the effects on the drow might be immediate. The culture might take a long time to change. And then it might not. In Erelhei-Cinlu (much more interesting city than the pale copy that is Menzoberranzan), there are already multiple cults and factions, although the spider-queen was first and foremost, so the culture might survive through other deities / demons, or there might be a revolution from the discontent or power-hungry...