Is Trixie's Season 6 plot a play on Lucifer's origin story?

So the basic Lucifer origin story is pretty simple: Lucifer's father abandons him, his mother sends him to Hell, and then he detests the both of them for eons until he comes to Los Angeles. That's literally Trixie's Season 6 story.

First, her father(s) do abandon her. Dan does it through death in the end of Season 5 (so not on purpose but still leaving her), and then Lucifer (a father figure of hers for five years) says goodbye to everyone else in his life in the finale, except for Trixie, and then he leaves.

In the bulk of Season 6, Chloe sends Trixie to a summer camp, we later see old Chloe on her death bed, Rory is there but Trixie is nowhere to be found. The excuse of the actress being unavailable doesn't even apply here because she'd just be recast as like a ~40 year old Trixie.

So her father figures leave, her mother sends her somewhere, and then she most likely ends up detesting her (and possibly Lucifer as well). Isn't that just the Lucifer origin story?