The odds are stacked against billionaire investor Eddie Lampert and his $5 billion-plus effort to resurrect Sears from bankruptcy, former Sears Chairman and CEO Alan Lacy told CNBC Thursday.

"Obviously, many people have said it, it's doubtful and unlikely that a retailer that goes into a Chapter 11 process comes out of it and stays out of it," he said on "Squawk on the Street." "It's rare that that's happened in retail bankruptcy history."

Once the largest retailer in the country, Sears has bled revenue and mounted debt for years, eventually running out of enough steam to cover a $134 million payment. Sears filed for bankruptcy last October after years of store closures. It's by far the largest of dozens of retailers to file bankruptcy since 2017, including liquidation of the iconic Toys R Us chain and department store Bon-Ton.

Lampert, who was once dubbed the "next Warren Buffett," stepped down as CEO of Sears Holdings Corp., the company behind the Sears and Kmart brands, after the bankruptcy. But he remained chairman.

Earlier this month, Lampert and his hedge fund won a $5.2 billion bid to buy the historic brand out of bankruptcy. Unsecured creditors are objecting to the deal and placing blame on Lampert, the hedge fund, and others for misconduct that they think played a large role in the chain's downfall. A U.S. bankruptcy judge is scheduled to consider ESL Investments' deal on Feb. 1 and, if approved, could save 400 stores and 45,000 jobs.

Lacy criticized the Sears stock buyback strategy before and during the 2008 financial crisis. From 2005 to 2011, the retailer spend about $6 billion to repurchase shares. He said the money should have been put back into the business.

However, Lacy said it was the Great Recession that really put the "nail in the coffin for this opportunity and that's obviously largely unrelated to Eddie's management style or anything." He added, "That was just a hugely impactful negative event, particularly for the Sears franchise which is much more correlated to housing turnover than anything else in the economy."

Yet, there is some hope that the 125-year-old department store chain could adapt to the retail landscape. But the company has a long ways to catch up as its hard to invest in online shopping since it hasn't turned a profit since 2010.

"It's possible, in my view, that [Sears] winds up with a going concern that's basically based online" because more stores could close post-bankruptcy, Lacy said. "[Online] seems to be one area that Eddie has paid a lot of attention to, invested behind ... and stores that are left probably do have some retail value."