I'll chime in and say the LC-1 is noisy. But I tied the sensor ground to the back of the head (1.6 ecu grounds) and separated the power ground.
The power ground believe it or not is now just on the firewall on one of the brake line lugs (I was getting desparate and tried it there) now it is noise free and happy.
I had no end of noise and resets when the two grounds were tied to the same spot (engine misfires with the MS too when the LC! heavy ground was anywhere near it).

How did i find the noise? I have an led bargraph in narrowband mode that shows rich/lean situations. When the LC1 was noisy, this thing would go haywire (it is grounded to the ecu points as well).