R.E Master of Malifaux: The terrain still exists on the table. I read that as she is not affected the Severe, Hazardous (and blocking when casting or charging) terrain traits, as these are all codified rules terms. Lilith does not treat the terrain as not existing, as she can't end inside a wall or something to that effect.
I had a whole big post about how I basically considered ending as entering and my support for that. However, after much thought and rereading rules, I think I've come down on the side of they don't take damage.
I would argue that the Incorporeal rule ignores terrain (and by extension its associated traits) for the duration of a move or push action. This would include the beginning and end of it as the only time the Incorporeal rule would not apply would be, logically, when you are not moving or pushing. It is functionally Hazardous terrain is being placed in contact with you after the action has resolved rather than you being placed in contact with it. There are other instances of this where you do not take the damage such as Jakuuna walking up to you or Ama no Zako casting her aura.
Flight however is slightly different, you would ignore Hazardous in the case of movement effects, such as your own walk or a Lure, however, you would not ignore it in the case of pushes, as pushes are not considered to be a 'move' in the rules sense of the term.
Both Incorporeal and Flying models would take the damage if they were placed in contact with Hazardous terrain, as placement effects are not movement effects either. (Rules manual, pg 60.)