The Sub power supply is sloppy and the fluctuating power needs of the sub are messing up the voltage in the A/C supply. The mains are being drawn down and bouncing way over the standard voltage by the sub.
I think that you may very well be pointing in exactly the right direction, Elizabeth. I'm thinking that what is known as an inductive kickback effect, from the power transformer of the sub's amp, may be putting a large voltage spike into the lights.
Inductive kickback, which results in what can often be an extremely large voltage spike, is what happens when the current through an inductance is abruptly changed. Power transformers have lots of inductance. The abrupt change might be related either to the sub's "fluctuating power needs," as you put it, or conceivably to the sudden change in line voltage that may occur when the lights are plugged in and start drawing current.
"Back emf," though, is probably not the best term to use for this. The back emf voltage produced by a woofer or other speaker driver results from a different effect -- the motion of the voice-coil continuing for some amount of time after the input signal has stopped or changed, which causes the driver to act as a generator until its motion gets back in sync with the signal.
Sprink, it would be helpful to know some further details: Does the fuse blow precisely at the moment the lights are plugged in, or at random other times? When it blows, is the sub turned on, and is it playing music?