Yeah, you will hear self proclaimed Audiophiles claiming they can hear this and that from things they do not understand...
The early generation of LED lighting, LED X-Mas lights and rope lights might create little noise on the power lines because they are a string of LED's connected in series with a resistor. Most of this type will also have some noticeable flicker because they are turning off and on 60 times a second.
Modern LED lighting has a regulator inside the bulb base, and powers the bulb from DC eliminating flicker and noise.
If you are worried about any audiophile acquaintances whining about your lamp making their ears hurt get a battery powered LED puck, or just turn the light off after you set the needle down.