Here is the block diagram showing how I've installed the Innovate Motorsports LC-1. The stock Narrowband O2 sensor has been removed, and in its place the LC-1 is installed. With months of measurements under my belt, I'm now confident that the Motronic functions the same with this sensor as it does with the stock sensor, it just programs and enforces a richer mixture.
Looking at the diagram you can also see that I've boosted the fuel pressure. This is an optional enhancement. When you shift the O2 setting from Lambda = 1 (stock) to Lambda = 0.94 as I've done, if you do nothing else the ADAPT box in the diagram will learn, over time, how much it needs to adjust the fueling to get the L=0.94 result. It takes time to adapt but eventually it does. Every pulse it sends out would become several percent longer.
The other option is to give the Motronic a headstart. One way is to add something like a BoosterPlug. It tells the Motronic the air is 20C colder and that results in a 6% richer mixture. The Motronic then has less adapting to do and gets to the final result faster.
The option I choose was to boost the fuel pressure by an amount that was equal to the shift in Lambda (plus an amount for E10 fuel) so that the Motronic would have almost no Adaptation work. (Fuel Pressure balances Lambda shift.) That means two practical things: as soon as you fire up the Motronic it's in the right ballpark; and every cell of the fueling table has been corrected (every pulse is affected by the increased fuel pressure), versus the coarser correction of the Adaptation process.
It seems like I've made a lot of measurements and tests to arrive at a simple solution for mixture enrichening but a side benefit is that a lot was learned about how the Motronic does its job and I've got a good confidence that the LC-1 implementation is compatible and that the Motronic is fully functional and operating as intended by the designers, just richer.
Tomorrow I'll add a block diagram for a Powercommander and Techlusion implementation.