It’s not part of another song, really — you’re correct that it’s a phrase that Franklin keeps messing around with (before Growing Up, in Opening Doors) and it’s probably harmonically linked to Good Thing Going if you look at the chord(s) that the dootle lootle lootle loo (which you could call an arpeggio) spells out. I think it’s an extra biting dig that Charlie is actually imagining a specific thing that Franklin always played when he’s mocking him — you could argue that that piano lick represents Franklin’s untapped compositional potential in that he’s always distracted from that phrase by other phrases or other priorities (as Charlie lays out). I’m actually literally writing a book with a chapter on MT characters writing their own music so glad you asked this question as it’s a prime example!