How to split isolated an audio trigger signal for processing by an ADC
A possible major source of noise is that you are connecting the (relatively) high-current LED power return and the analog signal ground together, so the voltage drop in the GND wire of the cable can introduce noise.

To reduce the effect, use two separate lines in the RJ45 connector/cable for the analog ground and the LED-power ground. At the microcontroller end, the LED-power ground should run directly to the power supply (or as close as you can manage), as opposed to sharing wiring with the microcontroller's ground (which is the reference for your ADC).

You will still get noise on the ground from the digital logic in the microcontroller, and crosstalk from the LED control signal; this is just a cheap improvement to your existing design.