When I placed a lamp next to a mirror where I can see "two lamps", does that double the light output? I know all the light that would have been wasted on the wall is now being returned so is it a yes?
No, the light output of a lamp is the same, you’ve just focused more of it in a particular direction. It’s the same reason flashlights have a cone shaped mirror around the bulb. If it were possible to double light output, then putting a lamp between two mirrors would make infinite light.