Because Snape asked him nicely.
After Snape overheard the part of the prophecy he did, he told Voldemort about it. Voldemort determined it referred to Lily's child, and Snape asked him to spare her. Then he went the extra step and told Dumbledore in an effort to save her. Per Snape's memories in Book the Seventh:
'Well, Severus? What message does Lord Voldemort have for me?
'No - No message - I'm here on my own account!
'I - I come with a warning - no, a request - please -'
'What request could a Death Eater make of me?'
'The - the prophecy... the prediction... Trelawney...'
'Ah, yes,' said Dumbledore. 'How much did you relay to Lord Voldemort?'
'Everything - everything I heard!' said Snape. 'That is why - it is for that reason - he thinks it means Lily Evans!'
'The prophecy does not refer to a woman,' said Dumbledore. 'It spoke of a boy born at the end of July -'
'You know what I mean! He thinks it means her son, he is going to hunt her down - kill them all -'
'If she means so much to you,' said Dumbledore, 'surely Lord Voldemort will spare her? Could you not ask for mercy for the mother, in exchange for the son?'
'I have - I have asked him -'
'You disgust me,' said Dumbledore, and Harry had never heard so much contempt in his voice...
Evidently, Voldemort gave her a chance to humor Snape. But when she gave him trouble he killed her anyway, not understanding the power of Snape's love for her, and in the end, that act, that single spell, was what led to his defeat.