My answer first take on this question was this--we know from the books that this spell, the killing curse, is unblockable. As far as ol' Voldie knew at the time, any other spell would have a chance of failure if she had any magical protection.
Second take is that she's an enemy and would definitely be an enemy after he killed her son. Why not eliminate an enemy when you have the chance.
Third take on it was that Avada Kedavra is actually a signature spell of Voldie's.
Fourth take is what others have already covered--he's an evil dude, and this is what he does.
As to the risk of alienating Snape, consider how close to the vest Snape played his cards--he may have asked for Voldie to spare Lily, but Voldie underestimated what effect that would have because, as we all know, he doesn't understand the power of love. The only reason why he did not kill her outright to begin with is because Snape asked. As far as V is concerned, he tried.
'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 -'
As you can see from this exchange, Snape may have asked, but he certainly didn't beg--to do so would have shown his hand and make him someone that Voldie might watch in future. Judging from Snape's overall actions and words throughout all the books, especially in concern to Voldie, he KNEW what a monster he is--and he KNEW that he could only push so far without raising suspicions--plus it's likely he already had the back up plan of going to Dumbledore to get Lily protection, something he could only do if his protest was framed in a way that wasn't "weak." Likely he told Voldie that he owed her something, or that he wanted her as a plaything later, rather than that he loved her.