The LC-1 controller connects directly to the WBO2 sensor, and controls the heater circuit. It also takes the data from the WBO2 sensor, and converts it to a simulated narrowband signal, which it then hands off to your ECM. I'm guessing you have a 4-wire O2 sensor (see graphic below)? The signal line should be the "O2 High" in your case. The "O2 Low" should be a ground.

Just to put things in perspective, here's another graphic showing typical 4-wire O2 sensor wire colors and pinouts:

That said, there are OBD-2 trouble codes for faults in the O2 sensor heater circuit. I'm not very familiar with the 3800 V6, so am not sure if its ECM uses those trouble codes. Maybe someone more knowledgeable with the 3800 ECM can chime in here. A couple possible solutions to that problem would be to put a dummy resistor in the heater circuit to fool your ECM, or maybe reprogram the ECM to ignore those trouble codes.
Or you could sidestep the whole issue by installing a second O2 sensor bung for the WBO2, and leaving the stock one in place. Just move the signal wire over to the LC-1.
Edit to add: I had to edit my post, because my experience using the LC-1 with a GM 7730 ECM is going to be a bit different than yours. But hopefully I can offer
something helpful here.

[This message has been edited by Blacktree (edited 02-18-2016).]