Sounds like you're going about it wrong. Fuel economy is best with increased efficiency. Leaning out won't make the engine any more efficient, it'll just create more heat thus less efficiency. You should be looking at cam timing and ignition timing along with making the throttle pedal more linear if you're looking to save fuel.

Assuming the engine ran exactly as it did at lambda 1, then yes. But you'll generate heat that has to be compensated for by less ignition timing, meaning less efficiency, meaning more fuel for a given torque output. You'd need to recalibrate every area of the torque management structure.

A true lean burn FSI runs AFRs closer to 45-50:1, but use a stratified injection mode that involves spraying the fuel literally at the very last millisecond. A homogeneous mixture of that AFR would melt things, quickly.

You're not running anywhere near the stratified AFR though. I did say that the stratified AFRs would melt things.

You say you've advanced ignition, but have you logged to see CFs and any other corrections that affect zwout?

Anyway, I can't offer assistance to able to run that AFR, it's not something I've ever wanted to try.

Please stop repeating this drivel over and over again.
The hottest burning mixture in homogenous mode is stoich, so lambda 1. Anything richer or leaner than that produces lower EGT on a gasoline engine... Take a gauge and observe...
Hence why most heat related engine damage occurs when running a mixture between lambda 1.05 and 0.9, and not when the fueling is so bad that it dips to 1.1 and up.

What OP is trying to do is a complete waste of time though. The difference will be negligible at best.
The way to really have more efficiency on FSI is to have a stratified burn thus massively reducing pumping loss. Creates tons of NoX though, there the temperature is also an issue due to the mixture not being homogenous, so you have hot spots and cold spots. The engine needs to be specifically designed for this though.