Power problem....each of these items uses power. At low RPMs the bulbs, and the motor too, need a certain amount of the battery power to function, as, at low rpms, even a good alternator doesn't produce enough to satisfy all items at once.
Check the battery, see if it is loading too. Cheap voltmeter will do this. Plus to plus pole, neg to neg pole, when she is running,and look for about 14 volts or so...if not, no loading is happening...see if this changes when you give it more gas....if not, maybe the rectifier is busted, or loose wires. Also, work your way back towards alternator and check connections etc, check clearance between rotor and stator too.
By the way...this is not normal....so you you don't have to jump to a bigger alternator setup.....until you find why the orginal setup is not working at least.
My guess is that the battery is simply finished (or not getting charged) and the alternator can't , at low speeds, keep up with keeping the motor AND the lights going......if all else fails...wait for the electro gurus to answer your question....