I've made the throttle switches connector/Co-pot connector cock-up myself before
but yeah, it's the white plug that goes on the white connector on the TB.
lambda shouldn't come into it as it doesn't get used by the ecu till the engine has got some heat into it.
What about the blue temp sender? has that been swapped out?
At this stage I think you have a few options: take it to an auto-electrician or garage with diagnostic equipment, or, find someone local who can bring their g40 round for a day of swapping parts over till you find which part(s) make yours work, or, start randomly replacing parts with new parts (but this soon gets very expensive!).
I was chasing a fuelling issue on my g40 a few years ago which almost had me at the end of my wits. Turned out the ECU itself had gone faulty and swapping it with a replacement sorted my issues.