You have lots of options. Yes, you can use both adaptors connected at the same time, esp. if you have 2+ USB ports free to plug them into.
The most simple would be to continue using the LOR interface and have a single Lynx DMX DOngle (flashed with Pixelnet) ... going into a smart string hub ... and using a smart string controller for each smart string your using.
Then control all using LSP 2.0 or using LOR sequence file + xlights (xlights support of pixelnet not officially released just yet). Either can support the dual interface setup.
You can also run the LOR boxes using DMX if you want, but then you would lose the LOR shimmer and LOR twinkle at the hardward level and use DMX software tinkle and shimmer instead (not quite the same). I would probably not use that DMX only setup, just because you would loose some capability.
You don't need to use the DMX-out from the smart string hub to talk to the LOR boxes, but thats an option if you decided to go DMX-only and Lynx only on the interface ... but probably not the preferred way, IMHO. You also would need a DMX to LOR cable built, since LOR using non-standard wires for the DMX signal.
I'd keep them separate if you can.