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mphillipps:
I assume from your description that the circuit is --- power company transformer 120-0-120 --- all wires and connections and other items from transformer to the main panel bus bars --- and the main panel . These are the common items associated with the lights and the hot tub. Thus, these items are the only common impedance relative to the tub and other loads. The remainder of the circuit from the main panel has a --- 240 breaker supplying the hot tub and no 120 loads from this 240 breaker --- from one or more separate 120 breakers the lights in question are supplied.
This arrangement would imply no neutral problem because no tub current flows thru the neutral. The entire problem is related to the impedance of the hot conductors from the transformer to the main panel, and this includes the internal impedance of the transformer, the service drop, meter, wires from meter to main panel, the bus bars in the main panel, and all joints in this path.
Solutions --- probably none relative to the circuit described above unless there are some obvious bad connections --- change the lamps to GE dimmable compact fluorescent lamps, maybe others are as good --- use a soft on-off control of the hot tub.
The GE dimmable CFL that I tested has very little intensity variation with respect to voltage change when a sine wave is applied. However, it cuts out at about 100 V. If the voltage dip resulting from turn on of the tub is not too great, then the voltage variations might not be noticeable. I have not run a transient test of an abrupt change from 120 to 100 with this bulb to see how noticeable it would be.
See my web site for plots of intensity vs voltage for several different lamp types under steady state conditions. Compare photo P14 (the GE with sine wave excitation) with P9 (a standard tungsten filament with sine wave excitation).
http://www.beta-a2.com/EE-photos.html
I have no knowledge of the existence of a soft on-off control for the tub. This would likely consist of a Triac phase controlled to gradually ramp up the current from 0 to max over maybe 20 to 30 seconds, and a similar ramp down at turn off. This would result in a gradual change in intensity that might not be noticeable.
Increasing the wire size to the tub would have no useful effect, and it would produce a minuscule worsening effect. The branch circuit to the tub is not common with the circuits to the lights. It is only common from the main panel to the transformer.
All my comments are based on the assumptions listed at the beginning.
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