lillia fae dawn alone on battlefield with a hidden card, can i move her, with the move trigger, can stay with the hidden card?

Yes — you keep the hidden card.

When Lillia moves, her "When I move from a location" trigger goes on the chain, putting the game in a Closed State. You only lose control of an unoccupied battlefield during an Open State (Rule 187.4.c), so you never lose control before the 3-Might Sprite token resolves at that battlefield. The Sprite is then there to hold the battlefield, and your hidden card stays put. (FAQ #10369)