I think Lolth was originally meant to have roughly the role Zugtmoy does in the adventure as released, the whole "elemental evil" thing being a front she's putting on and nothing to do with elementals, except incidentally to make the ruse more convincing, or the Elder Elemental Eye/God.
I interpret the "elemental" in "Elder Elemental God" to mean "fundamental", not "to do with the classical elements", whereas I interpret the same word in "Temple of Elemental Evil" as having the latter meaning. So the two need not and probably don't have anything to do with one another, even before we get into the erroneous identification of this entity with Tharizdun (which is apparently now canonical - well, so much the worse for canon then, I certainly won't be using it in my game).
Her motives in the adventure as originally intended by EGG are obscure to me, but in the sandbox game I want to run soon, which will potentially include a Zuggtmoy-less version of ToEE, these consist of destabilizing the region in preparation for the invasion that takes place in the G series.