I live in Casper and know Lysite. I suppose I know who you might work for...
The best waterfowl hunting is located southwest and southeast of Casper on the North Platte river. There is some public walk-in access on the river near Alcova lake that is pretty good for ducks. We also hunt geese in fields just off the river in the same area. (That stretch is also God's country for trout.) Last year, though, we spent more time hunting futher down river near Douglas and Wheatland.
Having said all that, the migrating birds come south along the eastern side of the Bighorn Mountains, mill around a bit near Casper, and then follow the North Platte over toward Cheyenne and down the Colorado Front Range.
The migration route takes them practically right over Lysite. You're right at the southern tip of the Bighorns. Good mule deer and Elk hunting too, if you can get somebody to show you up into the high country to the north.
P.S. Be prepared for some spectacular weather. Lysite has some altitude and tends to catch heck!