Thanks to Go Dairy Free viewer Destini for emailing this recommendation:
"Lazlo's on 192nd Street, just south of Pacific, in Omaha, NE was very patient and very friendly as a friend and I walked through their menu to find suitable choices with our various dietary restrictions. If you order thier burgers, steak, and chicken specifically as "dry grill", they leave the butter off. You also need to order the burgers without a bun. Being gluten intolerant, they also have a gluten-free menu. Even taking these both out, I felt like I had a handful of choices of delicious food to eat! (Some orders still need to be modified, such as "no cheese".) And they never made us feel guilty for taking so much of thier time! It was a refreshingly enjoyable expereience!
I should add, I'm not sure how careful you need to be for cross contamination, so if you have concerns I'd recommend calling beforehand."
They actually have three locations, two in Lincoln and the one in Omaha mentioned above (which was the location reviewed). See their website below for locations, phone numbers, and hours.