When Lady E. passed away no next of kin could be found so the building was turned into a school. Additionally, the school seems to be a place of interest for the ghosts, there is a portrait of Lady E. in the school's hallway and Jack and Parker found Lady E.'s old teddy bear at the school.
- Jossed: Vaughn said the building was originally a work mill.
In "Sink or Swim", Captain Archibald stated that Parker "will do just fine for the Lady" and tried to bring her to Lady E. It's possible that since Lady E. died she could want/need a new body and Archibald thought that Lady E. could use Parker.
- Jossed: Probably wanted Parker's soul since Lady E likes to turn people into ghost slaves when she gets ahold of them.
Parker shares her last name with two ghosts and Captain Archibald attempted to bring Parker to Lady E. for unknown reasons. Newbury is also a small town so it's possible she has some connection to any of them, like Parker could be Lady E's descendant or niece.
- Both confirmed and jossed: Parker is indeed related to a ghost but that is Vaughn G. Jackson.
In every single one of Jack's minifigure's there a brown strap with a dog bone shaped thing. Maybe Jack wears that as a Tragic Keepsake, even if his beloved pet (sort of) returned.
Either Bob and Linda didn't think too much about a middle name for their daughter or Linda just went ahead and gave her daughter her own first name as a middle name before Bob could suggest a middle name.
It's pretty common in fiction that some characters get named after the shows' creator(s), the producer(s) or their voice actors so I can see Parker's middle name being Lila after one of the show's writers, Lila Scott.
