Continuity mistake: When Harry is viewing Snape's memories, he witnesses a scene on Platform 9 3/4 between his mother and aunt Pentunia, in which Petunia tugs her hand out of Lily's grasp. Her hand is then back in Lily's and she tugs it out again.
Continuity mistake: When Harry talks to Griphook about breaking into Gringotts, Griphook has the Sword of Gryffindor in his hands. When Harry stands up to leave a few moment later, the sword is now beside Griphook's bed.
Answer: Voldemort more than likely saw Lily as a valuable bargaining chip. JK Rowling revealed in an interview that Voldemort always planned on killing James (which is why his death did not count as a sacrificial love). The reason Voldemort agreed to Snape's pleas to offer Lily a chance to live, is because he rewards his followers (always at a cost, however). Voldemort likely agreed only because he probably thought he could use Lily as leverage to ensure Snape was at his mercy.