LORELAI: Where’s his dad?
LUKE: Oh well, the great prize that my sister picked up at a Der Wienerschnitzel left her about two years ago, whereabouts unknown.
Wienerschnitzel is an American fast food chain specialising in hot dogs (even though the name refers to crumbed veal, which the restaurant has only served a few times). It was founded in 1961 as Der Weinerschitzel (which is grammatically incorrect as a German phrase). Although the name was changed in 1977, many older customers still use the original name.
Wienerschnitzel is predominantly located in California, which suggests that Luke’s sister Liz met her son’s father there, and that she and her son have been on their own for two years. It is worth noting that this back story changed during the course of the show.