Limited options but good
When visiting Mammoth Cave NP the Travertine Restaurant was very helpful. They understood the issue and we're happy to prepare things like trout and steaks in a separate pan, the salad does not even come with croutons and a good choice of sides (not fried). The food was very good. Ate dinner and had trout. The next day went back for lunch and had a cheese burger with GF bun and fresh fruit for the side. There is not really info on line. If you are visiting Mammoth Cave NP it is in the hotel right near the Visitors Center. Otherwise Bowling Green is the next best choose (40 min away). Note open May to early Sept - check web site.