Pat, I know that my D-Light RS485 dongles would work for DMX (not great, sometimes) but I never owned an LOR dongle.
As you said, a crossover for 1-2 to 4-5 works. That is is what I still use for some of my old D-Light DMX boards (AC and DC and Firefli)
Your most stable bet will always be to use an Open DMX or Pro DMX usb dongle. Better waveforms for stable output.