Yeah... I'm kinda worried about fighting, but momma duck (Vader) is really small compared to Lucy, and Lucy was raised by ducks, thinks she's a duck, and is basically a huge puppy dog. I'm keeping an eye on them though..
If Lucy stays broody she will hatch and raise the ducklings. However, if the momma duck is also broody you might try getting some of the eggs out from under Lucy, make her a nest someplace that is isolated from Lucy, introduce her to it and may need to restrict her movement from that nest until she accepts it. Otherwise, just keep her away from Lucy if necessary so that she does not challenge Lucy on the nest. Geese can be pretty aggressive when protecting their nest.
she is very protective of her ducks and not being able to watch over them would be very upsetting to her. 
She'll most likely think those ducklings are her goslings. lol it will be fine. I would let mama duck have eggs of her own though borrow some from Lucy and put her in a separate area from Lucy so Lucy won't take them back, once they start broody full time you can take as many eggs as you want they don't care as long as they have some to sit. only problem is if they are left together to hatch Lucy may take all ducklings when they hatch. And you don't want fighting because the little ones will be in jeopardy of getting injured.If this is Lucy's first broody I'd let her have no more than 6-8 eggs but if you don't have that many to split up between them then 4 would be fine . Just so they each have some.
I have one area that I allow 6 ducks in with 20 chickens and one rooster. They do fine together so far and it has been about a year. I do house the chickens and ducks apart from one another. The biggest risk is if a drake tries to mate with a chicken the chicken can be seriously injured or killed.
