From what I read, he theorized that internal competition was the only way to incentivize efficiency rather than being propped up by the rest of the company. Essentially, made each division compete for funding, which naturally lead to undermining and backstabbing— for example, the retail division started undercutting Kenmore with other brands— and eventually it all collapsed.

Lampert failed at the personal profiting part big time:

https://www.nytimes.com/2018/10/18/business/sears-edward-lam...

Probably one of the worst business moves in the 2000s.