Snape is over Lily. He's been coming to grips with losing his love for Lily ever since Harry gave Snape his (incorrect) explanation for Lily's treatment of him. The moment he kissed Rianne is the moment he finally decided to stop living and grieving for Lily and start living for himself.
The question is what it means for him to live for himself. Dumbledore's trust in Snape is based on his knowledge of Snape's undying love for Lily. If Dumbledore were to find out that that love no longer exists, he would (gently, perhaps) kick Snape out of the Fellowship. He would know that there was no longer any reason to trust him. And if Snape has gotten over Lily, he'll probably feel no real compulsion to help Harry in any particular way.
Quirrell, being a smarter Voldemort, knows what was driving Snape when he was working for Dumbledore, and he now knows that it's driving Snape no longer. That's why he had that little conversation with him in the woods; he knows that Snape is now a free agent who might once again be a blood purist loyal to Voldemort.
Voldemort would not likely welcome Snape back into his fold once Voldie reveals himself, but now that he knows Snape's loyalties are up for grabs, he won't hesitate to manipulate him and use him however he can until then.
Quirrell ... now knows that it's driving Snape no longer.
How?
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: