If I understand the question correctly (and I may well NOT be understanding it, in which case apologies for the useless answer! ;)):

This is usually caused by interference between the frequency at which the light oscillates and the speed of the rolling shutter in the camera. These days, most LED light systems are controlled by a PWM (pulse width modulation) controller, which cycles power on and off at a relatively fast rate to simulate variable brightness levels. In some cases the frequency of the cycling gets close to the frequency of the rolling shutter, which can cause problems.

The brighter the LEDs are with a PWM, the more time they spend "on" and the less time they spend "off". The dimmer the LEDs are with a PWM, the more time they spend "off" and the less time they spend "on". You will usually find that the interference patterns get worse with moderate to low frequencies.

There are two possible solutions. The first is to use a linear voltage regulator rather than a PWM to vary power to the LEDs. A linear voltage regulator is less efficient as it burns off the excess energy as heat, however it will not result in oscillations in the light intensity as a PWM does. Therefor, dimmer light is dimmer light, strait up.

The other option is to use an LC-filtered PWM. A filtered PWM will use an inductor (L) and capacitor (C) to maintain voltage and current in the moments when the PWM cycles off. You can usually find PWM controllers that are pre-built with filtration, however sometimes it's not specified. It is usually easier to find a linear regulator instead. Just make sure you use one that has a nice, large heatsink. ;)

I thought of a third option. Use a PWM that operates at a very high frequency. Something that operates at 15khz should avoid any problems with shutter interference.