Bedrockgames
I post in the voice of Christopher Walken
I don't think Lolth will get overthrown in her most iconic city, I think it's more likely the Rebel factions go into exiles. I mean what is Lolth and what will Drizzt novels be without it's City of Spiders?
If the Lolthites are desperate enough they will call on reinforcements from other Drow cities, and the Abyss/Demonweb pits.
I am not caught up on the recent books, but remember the Dark Elf trilogy. Menzoberranzan probably wouldn't be the most geamable place if it were made into a just city ruled by Drizzt. At least it would be only as gameable as any other city, not the terrifying place it functions as in the setting, so I think this sort of outcome seems more likely: just more factions of Drow, with many in exile or forming a rival city nearby.