Idk what youre trying to ask exactly but ive found the only thing that needs done to enable controlled lambda >1 is change your "lambdiag" value to whatever lambda you want to cruise at and raise lamlgmtm. No need to trick the ecu or sensor in any sorta way, although you might just want to disable open loop for low loads with RLLRUN if your ecu uses a narrowband sensor but maybe itd still be helpful to have narrowband lean adaptations, idk try it if you have a wideband gauge.

With narrowband you can just modify the voltage of the switch point.
I don't remember what the ID is, but I used it to run 1.15-1.2 lambda on LPG.

I made it switchable though based on whether LPG is on or off, otherwise it is not possible to pass emission sniffer test on gasoline and also it runs like shit at 1.2 lambda on gasoline, actually using more fuel.

Lamdiag is not a map, it's limitation in code