Transform Holdco LLC, an affiliate of Lampert's ESL Investments hedge fund, said it hoped to keep 425 stores open and 50,000 people working.
Sears continues its struggle to survive.
The hedge fund owner of Sears announced plans Friday to close 80 stores, including two in Maryland, amid a looming bankruptcy deadline.
Sears has had to close dozens of locations across the country after filing for bankruptcy.
Plans to close 80 additional stores were unveiled Friday, bringing the total number of closings to more than 260, which is over a third of its almost 700 stores. The closures will affect both Sears and Kmart stores.
The final decision on Lampert's bid will be made by the judge overseeing Sears. Earlier this month, he said he meant to offer $4.6 billion for the stores and assets.More news: Chelsea could decide Eden Hazard's future for him in January - Maurizio Sarri
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The company had almost 700 stores at the time of its bankruptcy filing.
Sears told workers this week it expects to begin liquidation sales at the 80 stores in two weeks. Sears' corporate headquarters was not answering further questions, either.
Lampert's bid won backing from Sears' existing lenders, Bank of America and Citigroup, as well as Royal Bank of Canada, which previously hadn't been a lender to Sears.
On Friday, the company announced 80 new closures as they try to avoid being shut down completely.
In this November 2018 photo, a sign in the window at Sears promises that 'This isn't goodbye, ' at the Livingston Mall in New Jersey.