Well it's not the LEDs, it's the rest of the circuit that's driving them. LEDs run off of DC. Therefore there is a rectifier circuit made of diodes. Simply putting AC through diodes doubles the frequency of the waveform but still leaves 'peaks and valleys', so a capacitor is used to 'smooth' that. I am guessing the sizing of the capacitor is the main culprit here. But i have no formal electrical training outside of what you get as an auto mechanic so there might be more to it than that. The 'grid' is treated, as far as i can tell, as an 'infinite source' where you don't necessarily have to build a whole lot of tolerance into your designs for 'dirty power' (i.e. a bigger capacitor). The impact of other devices in a house on the source would be like a 'drop in the bucket' on the grid, but when the grid is JUST your inverter and your house, it's more like a teacup than a bucket, and small disturbances are more easily noticed.
This is my layman's understanding. ?
As for what to do about it, you could either try different LED fixtures, try modifying the LED driver circuits, or feed them from a different source. For example, if the only thing on a circuit is LED lighting, NO receptacles, and the total circuit power is <100w or in the low hundreds, you could just feed the lighting circuits from a tiny inverter or certain kinds of UPS, dedicated to just those circuits.
