Lampert might have "saved" AutoZone, which AFAICT was the feather in his cap to make him "the next Warren Buffert", but if you asked me I'd be hard-pressed to tell you how the shopping experience changed. I speak from ignorance, and the laziness that prevents me from researching deeper, but I assume he did some accounting tricks, sold a few inefficient assets, etc. But as the owner of some old vehicles and a frequent shopper of auto parts stores, I couldn't tell you when Lampert took over AutoZone based on any changes to the shopping experience. So when it comes time for a new WhatsIt for the '81 VW, I'd just as soon go to the local NAPA because they'll probably actually have the damned thing.
This brings me to Sears: did he ever shop at his own stores, or was he busy pouring over the books and figuring out new ways to implement corporate versions of The Hunger Games? Because the shopping experience at Sears was never great, IMO, and it only got more depressing when Lampert took over. Tool quality went to shit, appliance quality went to shit, and the shopping experience sucks. You can juggle books all you want, but that won't get customers in the door. And if I do make it in the door, the lack of service and the dingy store will ensure that I never return.
So in summary, I argue that Lampert either got lucky with AutoZone, or what worked there did most certainly not work for Sears because at the end of the day customers ask themselves, "do I want to shop there?" And Sears in recent years gave customers very little reason to say, "Yes".
As a sidenote, WTH is he willing to throw good money after bad with his $4.4 billion bid? I'm stumped as to what rabbit he thinks he can pull out of that hat.