The OUTPUTS are labeled L/MONO and R (there is no such thing as R/MONO).
Just FYI: The L/MONO output is used when you are connecting the MOXF in mono to an amplifier that only has one channel. Doing so, and plugging nothing into the R output jack, sends both the L+R panned instruments to this single output... and keeps the phase between channels coherent.
If you plug something into the OUTPUT jack labeled R then items panned Left or Right will be sent more to one channel output than the other.

How to do it
If you wish to isolate your Lap Steel in the Right channel, you need to PAN the A/D INPUT to hard Right and do not use any SYSTEM EFFECTS (System Effects are communal and feed both Left and Right channels). You can assign an INSERTION EFFECTS to your Lap Steel. It will then arrive at the R jack

If you want to play an internal piano sound and have it only in the LEFT Channel, you can PAN it hard Left, but remember if you are using SYSTEM EFFECTS, normally they feed both Left and Right Channels, you can, however, PAN the System Effect Returns. This is found on the EFFECT CONNECT screen.

You can accomplish your goal if you maintain the panning throughout and pan the SYSTEM EFFECTS for the internal sound.

Plug the LapSteel into the "R" A/D INPUT
Set the AD INPUT part so that instead of MONO/STEREO is set to "RMono"
Pan the AD INPUT to the right "R63"
If you want to use any MOXF effects on your guitar use the INSERTION EFFECTS (only).

Whatever sound you want to play on the MOXF itself should be panned hard Left
If you wish to apply SYSTEM EFFECTs (Reverb and Chorus) make sure you pan the Effect Return hard Left.

You don't say what mode you want to be in on the MOXF but you can setup the AD INPUT in any of them.
For VOICE mode - the AD INPUT setup is found in UTILITY mode
For PERFORMANCE mode, and SONG/PATTERN MIXING modes - the AD INPUT setup is found in each program.

VOICE mode
Press [UTILITY]
Press [F3] VOICE AUDIO
Here you can setup the A/D input
PAN it "R63"
Set MONO/STEREO = "RMono"
You will be able to add SYSTEM EFFECTS only if you are 2CH mode, if you are in 4CH mode the REV SEND and CHORUS SEND will be unavailable (---)
I recommend you not use these Effects because you can use two INSERTION EFFECTS for the guitar if you want to and then pan the output.
You can access the Insertion Effects for the AD INPUT part here by pressing the [SF2], [SF3], and [SF4] buttons

Call up the internal Voice you want to use (VOICE mode)
Press [EDIT]
Press [COMMON]
Press [F2] OUTPUT
Pan the Voice hard Left "L63"

If you choose to use Reverb or Chorus, pan the EFFECTS by going to
[F6] EFFECTS
Press [SF1] CONNECT
Here you will find knob icons for "CHO PAN" and "REV PAN" - make sure they are panned Left "L63"

This will keep your signals isolated.