You're right, she does seem to be pretty friendly with them by the time she has Harry. We know from an interview w/ JK Rowling, that Lily was popular and well-liked. So the Marauders probably disliked her at first because of the way she treated them in the past and how she had treated James. But I like to believe that all of them grow up a bit after the WW incident. When they actually get to know her I believe they come to like her and the same goes for Lily. She's been treating them based on these ideas she's had about them since first year.Originally Posted by Midnight Storm
On the Remus front, she probably liked him best as he was the most mature and responsible of the four. While he could not control his friends, he seemed to at least know what they were doing was immature or wrong and did not participate. Also, he definitely liked Lily. In an interview JK Rowling was asked if anyone other than James liked Lily. She said (using my memory currently, not the actual interview, so I apologize if this is not spot on) that Remus liked Lily but never pursued her like James did.
I hope that helps!!