Apparently I have nothing better to do, so I found a way to blend the colored lights. It's not perfect, but it works well. I also noticed that I will have to do some post processing on my light map to blend the colors better. And my walls pickup the light from a nearby tile now, and it's not the expected effect. They now look like they get colored by a light on the wrong side of the wall.
The light map is only for static lights, I will have to run through a list of dynamic lights and calculate them separately.