Canon/Canon Point: Beetlejuice (the animated continuity, not the movie.)
Age: 13ish--potentially younger
Appearance: Lydia is a young teenager just out of Tween-dom, with very pale skin, black hair, and dark eyes. Her pallor is often accentuated by the dark clothing she prefers, or bright blood red. Her hair is just long enough to be pulled in a ponytail atop her head, or hang down to her shoulders loose. She often has either shadows, or make-up, around her eyes with pink on the lids, and purple around the rest of the eye. Her lips often appear dark-red, but again--that could be due to her pallor, or due to make up.
Lydia has a deep interest in the spooky and paranormal, finding beauty in things others might find gross, scary, or otherwise unpleasant. She's a very happy girl, all told, probably due to the fact that her mother and father love her, even if they don't always get her. It's unclear in the animated-canon if Delia is her mother or step-mother, but the two do seem to get along well enough and Lydia calls her mother. Her father, Charles, is neurotic and scared of almost anything, but does care deeply for Lydia, even with her obsession for the spooky.
If she didn't have this support, or her best friend Beetlejuice, it's likely that Lydia would be a very lonely girl. She has two friends at school (Bertha and Prudence) who seem to enjoy doing things with her, even if they are sometimes a bit more timid than she is. Certainly Lydia is teased enough, and occasionally outright bullied, for her interest in the supernatural and otherworldly, the off-beat--but most people seem to come to see the joy in it, or accept that she's nice and a good person anyways.
Beetlejuice is, without question, her best friend and much of the source of her courage and support, as well as her gateway to the Neitherworld (where she has more friends). There is even an episode that shows what the world would be like without BJ, and Lydia is a miserable, lonely, withdrawn girl. As it is, Lydia is the kindness to keep Beetlejuice in check, while she has enough of a mischief streak to enjoy his pranks, as long as no one gets hurt.
Overall, she is a happy, creative, and kind girl who searches for the beauty and joy in the strange and unusual, even if others don't always see it.
It's not entirely clear where the divergence between animated canon and movie are, but I'll try to summarize and offer a brief history for what we DO know about Lydia. She lives with Delia and Charles Deetz in Peaceful Pines, and attends Miss Shannon's school for girls. It's not clear when she moved there, although it is likely recent given that Lydia seems to have only two friends at school. It's a calm, and "normal" town, very unused to anything wild or out of the ordinary. At some point, Lydia met Beetlejuice, although it is unclear when this happened. She became friends with him, summoning him and the 'entrance door' to the Neitherworld via a chant. She can also summon BJ himself simply by saying his name 3 times, as also appears in her mirror at various points, to talk and keep her company.
On her visit to the Neitherworld, she befriended BJ's neighbors, who all like her even if they dislike Beetlejuice himself.
Sorry, there's really not much to her history.
"Summon Beetlejuice" Beetlejuice, her best friend, can be summoned via saying his name 3 times. Often this is dramatic, but it can be very simple as well.
"Neitherworld Chant" Lydia, when she is being formal and dramatic, uses a particular chant to summon Beetlejuice, and the doorway to the Neitherworld.
Though I know I should be wary, still I venture someplace scary, ghostly hauntings I turn loose...Beetlejuice, Beetlejuice, Beetlejuice!"
Photography Lydia is an accomplished photographer, with a dark-room in the basement of her very own.
Costume-design Lydia has designed costumes for her school's production of Romeo and Juliet (getting Shakespere's approval no less), as well as opened her own shop (with help) for clothing before. She also modified a pink-bunny costume into a werewolf costume, that her mother had bought her for Halloween.
Scenery design Lydia has helped design and promote a haunted house for her school's carnival, as well as assisting with school plays.
General Creativity Lydia is, in general, a very creative person especially with drawing, writing, and designing. Some of this may be due to Delia's influence, much of it might simply be Lydia's own personality. She's been showing playing guitar in a rock band quite competently, and to be good at Golf, as well as very skilled at video-games.
The animated cartoon verses the movie is somewhat inconsistent with the details, but it does not worry about that, or take itself too seriously. It makes jokes about the censors, or Broadcasting Standards and Practices, or breaks the fourth wall fairly regularly. There is some continuity, but not a lot. As such, Lydia is fairly versatile and adaptive, in how she can be played.
[Constructive Criticism prompt goes here.]
Out of Character: (alternatively, you could use OOC, instead of Out of Character)
"whatever you're using to describe here-example":