And your stock lights are different than mine. Not strange, just different. If you had a 2013 LC with OEM HID lows and LED accent lights your LED high beams would not work as DRL's, either.
What would be strange is if there were two 2013 LC's, one with LED high beams that DID work and one with LED high beams that DID NOT work; but that is not the case here.
So I hope that anyone with a 2013 LC is aware before they purchase LED high beam replacements that they will no longer work as DRL's.
It's no big loss for me because I stopped using DRL's the first time I pulled into a camp site at night and couldn't turn off my DRL's (my LC100 with mandatory DRL's). I use the parking lights now as DRL's. On my 2013LC that gives me the LED accent strip at the bottom of the headlamp housing as a DRL - I like it. If the parking lights are turned on after the engine is started, then they turn off when the engine is shut off and turn on again when the engine is re-started - no hassle. I can also turn them off any time I need to simply by switching off the parking lights
HTH