Presumably Liz Shaw leaves LV-223 in 2093, failing to realise that the cargo of the ship she's taken is more active than the casks she'd previously seen. En route to the Engineer homeworld she is impregnated by a facehugger and dies, crashing her ship into LV-426.
(No, not necessarily. It actually seems more likely that the vessel in Alien is just a different crashed Engineer ship. But it would be amusing if the navigator form from Alien was actually Dr Shaw all along.)
Original post on Dreamwidth - there are comments there.