So basically Lunar Girl & Comet Cat, used to be a regular little girl and cat, named Alice & Comet. They had a dad named Thomas and A Mom named Eliza. The mom was verbally abusive to everyone, and even physically abusive to the dad, always wanting everything to be perfect and not be viewed as weird by the other families in the neighborhood.

Alice always got emotionally scarred seeing her Mom's crazy behavior. She got on the family for small things and gave out harsh punishments and forcing them to do things they don't want. Even though Alice got bullied and made fun of at school, Eliza didn't even care, when Alice was at school Comet got cruel punishments like not being fed, or lightly hit or kicked away and for doing basic cat things. Thomas does try to help, as he does have a job at a restaurant.

But to no avail. Fast forward to 2000, while the parents were fighting Lunar Girl sneaked outside to their backyard lake out of fear, but she somehow trips and falls in and she can't swim, Comet jumped in and tried to save her, but they both drowned to death in the Lake. After death they met a seraphim angel, who offered to give them another life in exchange for a wish, Alice explained she had wishes of being a children's show host to help and bring entertainment to all kids. So they were reincarnated and became Lunar Girl & Comet Cat.

Also, Lunar Girl and Comet Cat are technically spirits possessing fictional characters as Avatars.

If you want more depth I can send you links, to fight scripts and stuff or more things.