Lilith is from a new story arc I'm writing at the moment.

She is a Nightmare, a type of domesticated demon created by fusing a Nightmare Soul (created by the future rider's own nightmares) with a corpse that matches the Nightmare's personality. Originally she was to be skeletal, but not only could I not draw that, it was too menacing a figure to write in.
Wyvern females are usually far larger and more dangerous, but as she's simply a Nightmare she's gentle and friendly. The saddle is for the look of it, if she lets you ride her, you aint falling off even if you're hit with a bus.