Adding a 110v circuit off 220v spa wiring
Can you come off the 50 amp feed for LED lights, yes. But what you have now is a non fusible disconnect, not a sub panel that can add another breaker for your LED lights. You can not just stick a 15 amp wire for lights under the 50 amp terminal and run your lights. (the wire would melt long before the breaker trips if there was an issue). You will need to take the 50 amp wire into a sub panel instead of the disconnect and then have 2 separate breakers for the hot tub and the lights that will be added.
It depends on your situation whether that is easier to do then running a new 15 amp line for your lights from the existing panel or even coming off another 15 amp circuit elsewhere in the house.