This sounds like a sexual innuendo. The surrounding context makes the situation sound like a late teen female discussing a younger sibling with her mum. Given that Lorelai is shopping for clothes for her younger sibling, it is safe to assume she is either legally an adult or almost so.
Lorelai's day of the week pants only go to Thursday. The literal meaning is in Em's answer. But the hidden implication is that Lorelai does not wear pants on a Friday.
This is potentially an off colour joke, given mum's reaction. The same phrase between peers would imply a certain availability on a Friday night.
The updated context that the show is the Gilmore Girls doesn't really change anything. Lorelai is an adult and during the show is in relationships with a number of different people. The conversation seems like a two digs at her mother, firstly that she is capable of clothing her own child appropriately and secondly suggesting a reason why she might not be able to that simultaneously puts the fault onto her own mother whilst calling back to the underlying premise of the show, Lorelai's teen pregnancy that resulted in Rory.
The TV Tropes page praises wordplay as one of the selling points of the show.
What really sets Gilmore Girls apart from other shows of its type is the heavy use of clever, fast-paced wordplay. Really fast.
Sexual innuendo is at heart wordplay, no matter what else it means for the characters.