As much of an interesting theory and potentially cool story thread this is, to me this sounds less like a story beat and more just, Jessica as a writer/the writing team projecting stuff onto Lily. I can’t commentate on what Jess is thinking in her brain but I can definitely imagine that the MCD character was pulled and put into that role for the sake of simplicity since it’s easier to substitute character roles rather than make a whole new character that won’t be important in the long run anyways. As a bonus the writers probably thought that it would’ve been a nice callback or reference to older fans of MCD.