Yes, Voldemort did try to spare Lily Potter during his attack on her family, offering her a chance to live.
The Sacrifice of Lily Potter
On the night of October 31, 1981, Lord Voldemort arrived at Godric's Hollow with the intent to murder the infant Harry Potter, based on a prophecy. Upon entering the house, he first killed James Potter. When he confronted Lily Potter, who was shielding her son, he gave her a choice: if she stepped aside and allowed him to murder Harry, he would spare her.
However, Lily refused to move. She stood firm, sacrificing herself to protect her son from Voldemort's Killing Curse. This ultimate act of maternal love and self-sacrifice, made when she was given a direct opportunity to save herself, created a powerful ancient magic that rebounded Voldemort's curse, destroying his physical body and leaving Harry with a unique magical protection.
Why the Offer?
Voldemort's unusual offer to spare Lily was not born of mercy, but rather an obligation. Severus Snape, who had a deep, unrequited love for Lily since their childhood, had overheard part of the prophecy concerning Harry. Realizing Lily was in danger, Snape pleaded with Voldemort to spare her life, promising his absolute loyalty in return. Voldemort, acknowledging Snape's request, decided to extend this conditional clemency to Lily.
The Unforeseen Consequence of Choice
Lily's decision to actively refuse Voldemort's offer and lay down her life for Harry was crucial. It was this act of choice—when she could have stepped aside—that imbued Harry with a powerful blood protection against Voldemort. This magical protection was so potent that it saved Harry's life multiple times and ultimately played a pivotal role in Voldemort's downfall. Lily's sacrifice is considered one of the most powerful acts of love magic in the Wizarding World.
For more details on the events surrounding Lily Potter's death, you can refer to resources like the Harry Potter Wiki.