Okay, this is a time travel fic that had (AFAIRemember) heavy Harry/Tonks leanings.

Here's what I can recall...

1) He goes to the past/Alternate Universe
2) He starts up auror training but doesn't not reveal his identity.
3) Lily serves there in some capacity. She allows him to use the Auror gym.
4) Tonks works there in some capacity. (Trainer, I believe)
5) James and Lily are married. Overtime, Lily becomes increasingly worried and fascinated by Harry, which incurs James's suspicious over her fidelity.
6) She invites him to dinner. There is some major quarrel.
7) Tonks defeats Harry in a duel because he apparates in from of his own curse. (Due to sudden flashback from the war)
8) Harry fucks Tonks roommate but then memory charms here.
9) Last chapter I read had Tonks, Lily, MadEye cornering Harry about his identity.

There.

 

http://forums.darklordpotter.net/showthread.php?t=8157
And it's Frank and Alice instead of Lily and James.