“Six-thirty in the morning!”

LORELAI: What are you doing?
LUKE: Fixing your porch rail.
LORELAI: That’s right. You are. You’re fixing my porch rail … at six-thirty in the morning!
LUKE: It was the only time I could do it.

The diner opens at 6 am, so what is Luke doing at Lorelai’s at 6.30? Has he just left Rachel and the rest of the staff to cook and run the diner while he wanders off to do handyman work for Lorelai? Or does the diner open later on Sundays?