The $3.3bn (£2.5bn) turnover US-headquartered print business went into Chapter 11 bankruptcy protection in the spring. Atlas emerged as the purchaser in September.
LSC employs around 14,000 staff and has more than 50 facilities producing magazines, books, catalogues and logistics.
In a statement, Atlas said: “LSC begins its new chapter with a strong balance sheet, an optimized manufacturing footprint and a more competitive cost structure.”
Atlas Holdings also owns packaging group AGI-Shorewood (ASG).
Timothy Fazio, co-founder and managing partner of Atlas Holdings, commented: “Atlas is the ideal fit as LSC’s new partner. Our roots are in paper – the investment that launched Atlas more than two decades ago was the purchase of a single paper mill in Indiana.
“Since then, our team has developed deep sector expertise in printing, paper and adjacent industries such as packaging and paper receipts and labels. This knowledge, coupled with our proven ability to transform businesses facing challenging market environments, positions LSC for a bright future.”
LSC was formerly part of the giant RR Donnelley business, which split into three companies in 2016.
The group had planned to merge with Quad/Graphics but the deal was called off in the summer of 2019 after regulators moved to block the deal.
Before it went into Chapter 11 LSC had short- and long-term debt of more than $900m.
In its most recent quarterly results, for the three months to September 30, sales were down by almost a quarter on the prior year at $628m and the business made a loss of $46m after restructuring, impairment and other charges of $56m.
LSC said lower sales volumes were partially as a result of the Covid-19 pandemic.