Beetlejuice is the Tuxedo Kamen style Guardian of the Senshi of the star Betelgeuse
And Lydia is supposed to be Sailor Betelgeuse. It's kinda in the title this one. Obviously he got corrupted by Metallia for the film, but got better by the series.
As a living child, Beetlejuice was Calvin
Think about it. They both love mischief, scamming people, have an affinity for striped clothing, they both have blond hair, and don't do well with authority. Beetlejuice loves puns, which he could have picked up as a child from his Saturday Morning Cartoon addiction.
As for why Beetlejuice's parents don't look like Calvin's parents, my guess is that Calvin died before they did. In their grief, Mrs. Calvin threw herself into her housecleaning, while Mr. Calvin did the same with working out, resulting in the ones we see in the show.
Hobbes (who turned out to be Real After All) was eaten by a Sandworm, and that's why Beetlejuice is so frightened of them despite having enough power to defeat them.
Beetlejuice is the ghost of The Joker.
The Maitlands' death scene was a false memory. Jane really wanted their house.
In the movie's afterlife, time moves quickly and the world makes a lot less sense. It would be pretty fair to say that reality is slightly off and subject to debate. The recently deceased are probably pretty confused and easily subjected to delusion. The zany slapstick death of Adam and Barbara is a fabrication they created to convince themselves someone they love didn't sabotage their car in order to collect from the sale on their house.
The Maitlands were infertile before they died.
Hence the look on Barbara's face and Jane's reaction of "I'm sorry I didn't mean it" when she says their house should be for a couple with a family.
- It would also give further significance to Barbara's affinity for Lydia, and wanting to stay with her. "I like that little girl."
- It's doubtful they knew for certain they were infertile, as Adam suggests "trying again" during their vacation, which seems a little insensitive of him to suggest if they really were. They may have just been trying for a few years with no success and Jane knew that.