So far I’ve discussed the Celestial Forms of grossly inhuman choirs of angels. The Lilim are quite different. They are described as looking like their corporeal vessels, only with green skin and tiny horns. This will work for most characters, but it’s worth noting that such a description will be inherently inadequate for Lilim with two (or more) grossly dimorphic vessels – or one which has lost its original vessel for one reason or another.
While the similarity between vessel and Celestial form is a good default, I would not force a player to stick with it. However, if there are gross differences between the two, that is certainly grounds to ask for a bit of background (or possibly even a work of short fiction)