Sears announced that it expects to begin liquidation sales at the 80 stores in two weeks.
Lampert's proposal is an effort to pull the company out of bankruptcy using his hedge fund, ESL Investments.
Sears is nearing a crucial deadline that could determine whether it survives.
Sears has told a bankruptcy court it has received several bids.
Lampert and ESL have been trying to buy the rest of Sears for up to $4.6 billion in cash and stock.
A Sears spokeswoman declined to comment.
Sears is closing 80 Sears and Kmart stores, including one in the Fox Valley.
The rules give Sears flexibility to extend the deadline or make other changes that might promote more bids.
Suffering from falling sales and heavy debt, it planned to close 142 of about 700 stores and cut thousands of jobs. When Sears filed for bankruptcy on October 15, it was still operating a little under 700 stores.
Wichita's last Sears department store will soon be closed. "We continue to believe that Sears' integrated and complementary businesses and brands can form the framework of a successful platform after emerging from bankruptcy".
It's unclear how many are employed by Sears in the Tri-Cities. Sears' corporate headquarters was not answering further questions, either. The hedge-fund investor pushed Kmart, which he'd bought out of bankruptcy two years earlier, to acquire Sears for $11 billion and then merged the two.
On Friday, the company announced 80 new closures as they try to avoid being shut down completely. On the Coast, the Sears at Edgewater Mall, an anchor retailer there, has already been demolished and replaced by a movie theater.