sounds like the variation in voltage output of your generator is not something that your LED's like, as is pretty common with LED lighting... sorry.
remember, too, that your LED's are commonly on the 12v side of the RV, meaning that while the Generator or Shore Power are in play, the Battery still provides support, but the CONVERTER takes that 120v power and brings it down to 12v for all your onboard 12v items and devices.... but, more than likely, since they work fine on shore power, your Generator is putting out variations that they don't 'like' so much.
There's nothing much you could do about it other than maybe try to add some type of Voltage 'conditioner' that 'smooths out' the variations.
'14 Palazzo 33.3 bunkhouse 34' diesel
KingTailgater2 Dish HD, 100w/5a SOLAR, BlueOx
100,000+mi since '14 - US, Alaska, Canada.... formerly Georgia, then NorthCarolina, now Alabama : )