I had hatched some guinea fowl the other month and that happened to one of them.... only with both legs. I was so sad when I saw it. I tried everything to help him. Every morning I would hold him in my hand and let him peck at a pile of food I had. Then, since he couldn't walk, I would hold him above his water and let him drink all he wanted. That was a mistake. He was getting lazy. I did some research, and learned that if you take a pipe cleaner, and make it into an 'M' type shape so that it looks like the duck's foot, you can somehow attach it onto the bottom of his foot so that it flattens his foot out. Then you have to force him to walk to get the strength into his lame leg. After a couple days, it should start working.
I don't want to scare you, but my chick died after a couple days. Maybe it will be better with your duck because only one of his legs is lame.
Hope this helped.