So Carol is only going to be living out of her car and magical diner locker until such time as Shep's "music video" is on MTV, of which she is the star. What's a music video? Ask your mom. It was once a much-touted "new art form," like a Rubik's Cube, which Owen is playing with, because he's a genius. Shep is also a genius, a musical one, and Lily asks why Carol hasn't given their demo to Rick Rhodes, if they're so good. Owen catches part of this conversation about their totally rich dad in the music industry, but is such a genius that he doesn't seem to find it important.
Carol turns the radio up and says to keep quiet about their family. "Why do you care what they think? And besides, being us is awesome," Lily says delightfully. Carol says the usual, how the strings are attached and how people outside the family treat you differently. "Yeah: better." Lily is SO GREAT. Carol snarks that she sounds like CeCe, which Lily awkwardly rewords to be some kind of dumb complaint about Carol ditching her, and Owen saves the day by whispering from the backseat in a caring voice, "Hey. I think we're here." Like if he hadn't said that, they would have kept fighting and what, driven past the mansion they're going to?
Lily shows up to apologize to Rufus for, um, parenting her own child in a way she thought was appropriate, because that's what happens now. They sit on his couch and she talks and talks and talks until he decides that she's talked enough, and he can give her condescending little taps on the arm like how she is capable of one day growing to be a better person than the shit-ass worthless person she is today, who would do something like have her own daughter arrested, like he tried to do a few episodes ago, and that if she wishes and tries hard enough to earn it, maybe one day he'll deign to marry her, and live off her at the age of like fifty while he decides what his fourth career should be, but in the meantime she should forgive her daughter (like she already did three times at the beginning of the episode) and her mother (like she's obviously going to do for no reason at the end of the episode).
Carol and Lily climb in through a window in a random closet in the mansion where the we still don't know what is going on is going on, and Carol explains that the director of their music video is holding the tape hostage, so Carol's going to like get it or whatever. Any time I type the name Carol, assume that Shep is around somewhere pretending that he's her boyfriend, and she's explaining to him at various volumes that they are not dating. There is no need to imagine that it is particularly funny.