A/c makes the lights turn on and off! No Joke!
Which country, Michael? USA, by any chance, judging from your jargon? If so... I think you may have a grounding issue at the panel or at the line coming in from the pole. I've seen similar issues, and issues with lights burning EXTREMELY brightly for a short while before they burn out, from just such grounding issues.

Especially if the AC and the 1st-floor lights are served by breakers near the bottom of the panel, or from a separate subpanel... in the former case, the grounding problem may be inside the panel itself. In the latter case, it may be in the subpanel or the wiring leading to it.