The OP's assertion about Lolth fits in 100% as canonical, especially when one reads the War of the Spider Queen series (particularly R.A. Salvatore's intros) and in the Rise of the Underdark plotline-wherein the drow try to invade the surface as a part of Lolth's bid to become the new goddess of magic-the intro video, narrated by Lolth, explicitly states that she brought the drow to the Underdark as sort of crucible, to forge them into perfect weapons.

Also, 2e's monster Manual said about the drow that since their training regimen is so harsh that no drow is ever encountered below 2nd level. Any drow that can't hack it gets executed.

So...yes. You're correct about her.