Luke didn't need Emily's approval, but: 1) confirmation that the whole Chris thing was just Emily 2) Emily's confession that she will no longer meddle in their relationship
I would also have doubts in his place: if Chris hadn't been at the wedding, he wouldn't have found out that Lorelei had been drinking tequila with her ex the night before (yes, whatever the reason was, first the child, then dad died, because maybe something else would happen), they are with Rory They lied about that night, why Lorelei had a hangover then. if Lorelei had told her right away and not made up nonsense, then they would not have had any misunderstandings and Chris's presence at the wedding would not have stuck out like that. Lorelei is comfortable blaming Emily, but you still need to clearly assess your sincerity in the past
@MariaDisney: I think Luke didn't need her approval, but just a push. And Emily served them exactly. Because there wasn't enough time for him to come back during the musical. Then there was a whole series of angry walks. Maybe he was angry at himself.
Emily is super nasty. She pretends to be the arbiter of human destinies, because, apparently, there is nothing else to do. And she was also offended by Richard's mother-and she was the same!
1) confirmation that the whole Chris thing was just Emily
2) Emily's confession that she will no longer meddle in their relationship