I dare anyone to come up with
(A) a reasonable way that First Impact could somehow have destroyed Lilith's Spear while not destroying Lilith herself.
(B) a reasonable way for Adam to end up a "drowned corpse" pose perpendicular to the Spear with an incredible length of tines directly beneath her if we're meant to believe she was just minding her business one day and the spear decided to stick her in the back.
A) Maybe the spear left of its own accord? And in the sense that was "destroyed," perhaps the spear we see throughout NGE, with its double helix shape, is actually a fusion of both spears? And thus the spears came together and got Adam for some reason?
B) To answer this better, maybe the spear(s) was following some weird programming from Lilith or decided to lock Adam into a state where she'd already been inactive for a long time. I mean, what purpose does an already perfect being have anyway? There was no challenge to necessitate creation, nothing to strive for, so Adam laid dormant doing nothing. It's rather refmicnisnt of the various ways Shinji hangs his head in despair, plus his disposition about basically being nothing in a world of "perfect freedom" in ep. 25/26...
Point being, I like to think that the spears are just long red pointed sticks (which is why the term lance works so well here) and then the version we see with its odd behavior (subduing Adam, subduing Lilith, killing an Angel, connecting with Unit 01's core, becoming the Tree of Life, changing shape again) is a hybrid.
Also, wasn't there some bit about it being moved back and froth from Antarctica to the Middle East where the SSDSCs were found during the Katsuragi expedition just prior to 2nd Impact? What was that about? Because I have something of theory on that as well...