Is it possible to power/turn-on LED lights through a lamp switch?
The easiest way to run an LED off of 120VAC is to use an LED that's already designed for 120VAC, like a 120VAC LED Panel light. They come in a wide variety of sizes, colors, and form factors.





(Photos from Digikey's catalog). 

Just keep in mind that 120VAC is dangerous, and if you're not actually going to panel mount them where only the front of the LED is exposed to the user with the rest of the LED shielded by an insulating or grounded panel, make sure that you keep them safely isolated so the user can't inadvertently come into contact with the back side of the LED housing or wires.