S4, E12: Luke is wary when his flighty sister Liz (recurring guest star KATHLEEN WILHOITE - "ER") arrives for an unexpected visit. Lorelai promises Jason that she will tell her parents about their relationship, but she reconsiders after Emily comments about how laughable it would be if Lorelai and Jason began dating. Meanwhile, when Paris confesses to Rory that her affair with the professor is becoming serious, Rory reminds Paris how badly she is treating her boyfriend, Jamie (BRANDON BARASH)--so Paris breaks up with Jamie. Finally, Luke discovers that Jess' (recurring guest star MILO VENTIMIGLIA) car is missing and reports it stolen, but he later discovers that Jess has come back to town to pick up the car. Rory sees Jess sleeping in his car but walks away without speaking to him.