I got your file (didn't realize you posted it)...I just saw your screenshot earlier and happened to check back by and saw the file there.....
It's a simple fix....your lights each have a radius of 5, which causes them to intersect with the objects. I read somewhere that if your lights intersect with the objects, strange things will happen....well this must be what 'strange' is!
I went in and changed the light properties for each to have an Intensity of 1.5, Decay Rate 0.25 (You can lower that if you want.), and a Radius of 1.0.
Just a question, do you have the render preview window plugin? That allows you to see a snapshot of what your render will look like so you can tweak things before doing a final render. If not, go to Tools Menu > Scripts and Plugins Manager and choose the Install Tab. The Scripts and Plugins Manager will automatically go to the Repository and tell you what's available. Download any/all that appear interesting, but for this exercise, choose Preview Plugin....which is under the Plugins folder of the Install Tab. Select it and then tell the Plugin Manager to Install it. Close the Plugin Manager and restart AoI. On the next start, you should have a little preview window on the right side of the screen. When you want to see a preview, hit Settings > Renderer in the Preview Window area and experiment with the various render settings. Then, hit the preview button and a preview will be produced. It's a nice feature and will keep you from getting some 'surprises'.