Welcome to the Werkz, hopefully you can enjoy your time here.
If its a new radio, that an amateur has installed, I'd put money on the "lights on" lead from the old stereo has been connected as the ground lead on the new unit. I had a similar problem when I was younger after I installed a new stereo. You can test this fairly easily by disconnecting the stereo and trying your lights out, if they work, get hold of a multimeter and check the connectors on the stereo plug until you find out which one goes live when you turn your lights on and off, change it to a proper vehicle gound.
Good luck and let us know what you find.