The Sears Auto Center will close in January.
Lampert's hedge fund, ESL Investments, had previously stated earlier this month it was willing to buy Sears in full with a $4.6 billion proposal. When Sears filed for bankruptcy on October 15, it was still operating a little under 700 stores. Any bid to purchase it must be approved by a bankruptcy court.
Another store closing was announced for a location in Muskegon.
The Charlottesville Sears store is among those listed to close on MarketWatch.
Lampert has been putting together a $4.6 billion offer to maintain control of a chain of about 500 stores under both the Sears and Kmart brands.
The troubled retailer announced plans Friday to shutter 80 of its Kmart and Sears locations by March - on top of an additional 182 it had originally planned on closing in the first quarter of 2019 as part of looming bankruptcy proceedings.More news: Bomb strikes tourist bus near Egypt’s Giza pyramids, kills 2
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The company says these closures are in addition to the shutdown of 40 unprofitable stores expected to be completed in February.
So far a hedge fund controlled by Eddie Lampert, Sears' former CEO and now largest creditor, is the only entity to publicly disclose a plan to bid.
Lampert bought Sears and merged it with Kmart in 2005 to form Sears Holdings. One was a joint bid from Tiger Capital Group LLC and Great American Group LLC, and another came from the team of Gordon Brothers Retail Partners LLC and Hilco Global Merchant Resources LLC, the Journal said.
Liquidation - which would have been halted if a buyer stepped forward - is set to begin in two weeks.
ESL said that should its bid be accepted, it expects the company to emerge from bankruptcy. His plan would retain the jobs of 50,000 of the 68,000 workers employed by Sears at the time of the bankruptcy filing. He's shuttered hundreds of money-losing stores, cut more than $1 billion in annual expenses, and spun off units such as Lands' End Inc.