Interfacing with existing outdoor lighting

I have the Ring hardwired floodlight, camera, motion detector installed and interfacing with my Ring security system. I have all my outside lights connected to my old security system, they would go on when my old sensors detected movement. I have them all connected to a 110 volt relay. They used to work flawlessly on my old pre-Ring system. I would like to interface them to the Ring floodlight system such that when the flood light goes on it will trip the relay and all my lights would go on. I thought of using a smart outlet but it looks as though only 'lights' will interface with the Ring floodlight. Any ideas??? Thanks, Jim