The lights out won't kill the cyano and unless you tackle to source you won't be rid of it. What are your parameters specifically nitrates and phosphates. Even if these are reading zero doesn't mean that you don't have a problem. Two fish such as these with minimal live rock, minimal flow and crushed coral substrate are all part of the problem, my bet is you are not running a skimmer either. You need to increase the amount of rock to help in filtration, increase your water changes and start with a 25% change, increase the flow in the tank and possibly think about changing your substrate to sand rather than crushed coral which becomes a nitrate trap after a few months as you are experiencing. You don't mention any clean up crew either, what is eating any detritus and food that isn't eaten? You may want to reduce your feeding and the amount you feed. All these things may help.