If you want to pull the wires for the B1S2 HO2S out of the harness, you can.
I believe I've concluded that LSJ's do some very slightly weird things without the rear O2 that are, in the end, inconsequential, but can be confusing if you don't know what's going on. When idling, the computer will occasionally command a dip and then rise in Commanded AFR (like 30s at 12:1 and then 30s at 17:1) that I'm pretty sure is some B1S2 calibration or check routine that HP Tuners doesn't have access to turn off. I use it as an opportunity to get comparative wideband data at idle as I'm logging fuel trims during CL operations and this routine will kick over to OL. Not a big deal, just weird and confusing if it comes as a surprise.