Yes, but now the receptacle has be GFCI (as per 210.8 (B) 8). The conductor to the receptacle (served from the 20 C/B) has to be #12Awg, and a single receptacle on a 20A branch service has to have a 20 amp (not 15A) rating too! (as per 210.21(B))
Just swap the 20A C/B for a 15A C/B.... or....
Will your LED lights drawing __amps ever overload /overheat the #14 Awg cable?
Will you be able to sleep at night if it's not to code? ....but somehow be able to sleep at night if it's to code but you use the loophole that still uses the same ___amps running down the same #14 cable?
This is where someone mentions liability and ...and the "What if's" & getting lawyers involved!