Q1 (and later novels based on it) allowed adventurers to kill Lolth in the Demonweb as part of a campaign based on Greyhawk.
I'd have to double-check the FR sidebar, but offhand I'd say that unless there is more than one Lolth and more than one Demonweb, killing her in the Demonweb kills her no matter what world you are from. It would be one thing to say that killing Lolth on Faerun is different from killing her in Greyhawk, but killing her in her home plane of the Demonweb is supposed to be what is necessary to finish her once and for all.
During Q1, Lolth was "only" a Demon Lord. Later on, Loth become a demi-Goddess and currently is a Lesser Goddess. I have no comment on what her status is after the War of the Spider Queen novels (and the module doesn't say anything relevant), but reading between the lines I have a pretty good idea of what is happening.
Greyhawk canon is vague on whether Lolth actually died in Q1, however we can surmise that G1-G3, D1-D3, Q1 happened and that adventurers slew what they thought was Lolth. What they slew might not have been the real Lolth, it might just have been an avatar.
Alternatively, she might have really died, but she came back from death somehow with even greater powers (dying as a demon lord, coming back as a lesser goddess) through the worship of her fanatical followers.