Mary, the agent showing Luke the apartment he’s considering, assumes Lorelai is Luke’s wife. This is a common trope from sit-coms and rom-coms, showing that the couple must be meant for each other, because everyone else can see it.
Lorelai looks very happy and comfortable pretending to be Luke’s wife. Luke’s expression is somewhere between “deer trapped in headlights” and “please don’t get an erection”.
The Annotated Gilmore Girls 