She drops from the adventure. She is not in a box/crate. Once she drops she is in your inventory (you see her fall from the adventure, she has white hair). I wrote more about this in post 1
Once she drops you'll get the next set of goals (assuming you've done the debris and tree goals too). If you have Lila's lotion goal, when you Entrust Lila to Lady Greselda, she disappears from inventory.
See my post above for glitch report.