Go to the review site and click the "Useful" button for all 1-star reviews (and write a review if you are inclined but you have to sign in for that I think)
https://www.yelp.com/biz/the-red-hen-lexington-3
Contact their "partners" and let them know they are proudly doing business with a despicable organization
https://redhenlex.com/about/our-partners/
Do a search for owners Stephanie Wilkinson and John Blackburn (ie stephanie wilkinson red hen) and find some shit out about them and let your creative instincts run wild)
People also talk about making fake reservations and such, I don't know about that. Another idea is to go there and raise hell and get news coverage.
But: The idea is not to just harass but cause a PR problem which may well be enough to put them out of business.