Here is my spec for the rest of the episodes
In 7.18 we know that Luke and Lorelai talk and apologize for everything.
7.19, It's been awkward and stuff with them and the returning to the diner and car shopping and all of that. They fight, get a lot off their chests about what happened to them. They kiss, it's freaks them out a little bit and decide it's too much too soon for them
7.20 Lorelai invites him to go to the karaoke bar. She sings the song. They have a moment.
7.21 Lorelai comes back from the graduation, it was weird and awkward with Christopher and just proved to her how wrong it was and how much she does love Luke. They talk, Luke proposes relationship/marriage whatever. I see this being a cliffhanger for that.
7.22 They are finally in a full-fledged relationship and celebrate Rory's graduation and their finally getting back together.