The problem is poor design of the switching system. It uses a triac with
duty cycle control of the current. Since it switches the lamp on late in
the cycle, there is a big transient each cycle.

It's an old design. I don't know if the newer ones are any better. I would
think it had to mee FCC part 15 to be sold; how old is it? Talk to the
manufacturer and the FCC to find out if it's still being sold.

About the only thing you can do is shield and filter, but shielding would
make the lamp rather useless. If you are concerned about 7 MHz noise then
better use filtering components that are effective at that frequency.

73, Bob