Has your RV always done this? There are a couple of easy thoughts I have that could help. First is that you could try (if your light fixtures allow for this) to replace one of the led bulbs for an incandescent bulb as doing so can stabilize the entire circuit of led lights (pick one out of the way and use a small incandescent bulb (low wattage like a dome light size). Second is that if the pump was directly connected to the battery (instead of the fuse panel) and with its own fuse and wiring, then the voltage would be more stable for the led lights (perhaps using a relay would work best). Third, many led bulbs are known to be more vulnerable to slight voltage fluctuations and therefore new (different) bulbs could help but again, who knows which bulbs are better. Fourth, my last thoughts for now is that it is possible to install a capacitor at the pump that would help stabilize the voltage (just like a car audio capacitor), but that comes with other concerns and not what I would recommend at this point but something to be aware of. ~CA
My suggestions above are with only after making sure all the connections are good, you may want to run a second ground wire to the 12v water pump as a thought and as a test, especially if this is a new problem.