Belmont Run Apartments for rent in Lexington, KY on ForRent.com: (866) 640-4765 - Availability, pricing and special promotions subject to change daily. Belmont Run offers remodeled apartment homes in a great location close to UK. The kitchens have been updated with beautiful cabinets, countertops, appliances, upgraded lighting, and a breakfast bar. The large apartments offer new carpet and flooring. We have onsite management so stop by for your tour today.