Sigh...
Lots of confusion here!
I've said it before and I'll say it again:
Lean burn (or stratified charge) mode does NOT apply to the Mazda DISI engine. This engine NEVER uses a A/F ratio leaner than stoichiometric under any steady operating condition (cruise, idle, etc.)
As far as A/F ratios are concerned, think of this engine no differently than you would a port inected engine. If anything, the cooling effect of the direct injection may allow for a SLIGHTLY leaner A/F ratio under some operating conditions but that's about it.