Ground loop between Pc and projector via VGA cable
That approach is common in audio and industrial sensor signals for the reasons you've identified. The screen is usually left connected at the transmit end and disconnected at the receive end so that may be worth a try. Get a short male-female cable to hack and install it at the projector end.

We're short a few details on your setup. What kind of lights? Fluorescent, incandescent, dimmers, etc.

Ground loops cause problems because of either a) a difference in ground voltages between the signal source and destination or b) because of induced currents in the loop due to EM interference. 
Something that may be worth a try is to power the PC and projector from the same socket. This should eliminate any ground potential differences. A temporary extension lead should be good enough to give an indication.
If you can run the mains cable close to the video cable it will reduce the cross-sectional area of the loop and that may help too. (I know this is usually not considered good practice and you may get some switched mode power supply interference.)