Answer: She wanted to be with her mom who had passed sway.
It's never stated that her mom had died. There could be a possibility that Charles and her mom got divorced. The first two answers are more likely.
I've heard the interpretation that Delia really is Lydia's biological mother, but they are very different and don't get along, so Lydia pretends that Delia is a stepmother.
Answer: She wanted to be with the couple, she did not think of the repercussions.
Phixius ★
She was incredibly depressed. She wasn't happy anywhere and she didn't fit in with her own family or anything they were trying to do. She was a goth girl. The realm of the dead and the macabre seemed more a place for her. When one sees the "Netherworld," it kind of seems like a more interesting place. But... upon closer inspection, it's not really all that different from our world.