Is the remote IR or RF? If it is RF you will need to switch it to IR, if you can, the Beam only has an IR receiver.
As the ARC port is not recognized you might have bigger problems still mind you...
Remote “Pairing” usually refers to a Bluetooth connection between two products. In this respect is not possible to “pair” with a BEAM because BEAM does not support Bluetooth control.
In the LG setup you should be able to indicate that you want to use its remote to control an A/V receiver (using IR commands). In this setup procedure you will be asked to pick a manufacturer. For your purposes this is an arbitrary choice, just don’t pick one that you presently have nearby. Now, you can train BEAM to accept these Volume commands from the LG remote. If you have a cable box, specify the same receiver and you’ll be able to control Volume with the cable box remote too.