A 1-1/2 HP motor operating at 115 volts will draw about 60-100 amps on starting. Running will be about 15-20. Before we get too carried away with the loose neutral idea, first consider the overall layout of the system.
1) How far is the utility transformer from the meter?
2) What size are the conductors from the transformer to the meter?
3) How far is the pump from the meter? Is the pump fed directly from the main panel?
4) Do all the lights brighten or dim? Is it just a little, or a huge amount of brightness or dimming?
5) Does anything else that has a motor cause the lights to brighten or dim? Like the washing machine, dryer, dishwasher, or disposer.
If the utility feed is overhead, and longer than 50', the situation might be normal. A 1-1/2 HP motor operating at 115 volts on a residential system is very close to abusive. The best solution here would be to re-connect the motor for 230 volts, and change the breaker to a 2 pole. (assuming nothing else is connected to the pump circuit).
If the motor were to be operated on 230 volts, the lights would not brighten at all, though slight dimming might be noticeable. #14 wire would be the code minimum, and a 25 amp breaker would be the code maximum. This would be one of the rare times when an oversized breaker is allowed by code.
We can help better with a bit more info.
Rob