RORY: How many meals is it gonna take ’til we’re off the hook?
LORELAI: I think the deli spread at my funeral will be the last one.
A deli spread is a buffet of cold cuts and other delicatessen foodstuffs. Presumably this is standard fare at American funerals (more correctly, the refreshments that are served after a funeral service). Lorelai is predicting gloomily that she will be obligated to her parents for the rest of her life.
The Annotated Gilmore Girls 