She doesn't like to talk about it much, but she's actually a lycanthrope. She transforms every time the moon is full, and has no control over herself when this happens.
No one knows why she's this way. Starswirl hypothesizes that Luna's connection to the moon has something to do with it. It'd be different if she was bitten, but she was born this way and it's all she's ever known.
On nights without the full moon, Lykos' job is to monitor the dream realm in her mother's place, swapping every other night with her sister, Evangeline.
During the day, Lykos herself is a very aloof pony. She doesn't do well in social settings, and prefers the company of her closest friend and siblings. Lykos isn't the best behaved mare, often letting her canine instincts get in the way of her pony senses, which can be off putting to most ponies.
Luna and Rainbow Dash love her dearly, and try their best to help her when they can.