Any fuel being wasted is likely to improve emissions. For instance, my MX-5 will retard timing significantly during the first 15 or so seconds after a cold start, to blow still-burning fuel into the catalyst, to light it off sooner.
There really isn't any magic to engine tuning. You have your air fuel ratio (which you can see with an OBD reader), which could be worth 0-5% with a very lean tune. You have your ignition timing, which, if too retarded, would burn vales, and if too advanced, would cause knock -there might be another 2-5% on the table there at WOT, but likely zero at cruise. You have EGR, which can either be from a valve or by advancing cam timing on VVT engines - there's maybe 1-2% to be gained there. And, that's it. Everything else is mechanical.
Lean burn doesn't allow normal catalytic converters to work properly. That said, it's generally worth less than 5% extra fuel economy. You're not going to turn 18mpg into 28mpg with a tune. Maybe 20.
The main issue with running a lean burn tune on an engine not designed for it is that it slows the flame front down significantly. You have to advance ignition timing a lot, which ends up causing a lot of the combustion pressure to build before the piston reaches the top, creating negative work, negating most of the gains you'd otherwise get. Factory lean burn engines have some head and piston and valve design tricks to help speed up combustion of lean mixtures.
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