I am trying to program the LG remote that came with it
to my Motorola DCT6416 III DVR from Cabel One.
Any codes you might get in this forum won't help you with the LG OEM remote as they're specific to UEI brand of universal remotes.
I have tried 201,038,039. Those are the only codes I
have been able to find online that reference Motorola
You can probably try codes for General Instruments to see if any of them work.
Another option would be to get a UEI universal that will support both the TV and DVR.