The lawsuit also says Foster "threatened to expose the Ball family with false information to the public" after he was confronted about the missing money.
Ball severed ties with Foster following the feud, per Ramona Shelburne and Paula Lavigne of ESPN.com.
Foster owns 16.3 percent of the company, but according to the lawsuit, the Ball family had no knowledge of the fact that he had gone to prison for his role in a Ponzi scheme.
They now believe he only got close to the family to steal money once Lonzo made it to the NBA.
"I've always believed in the best in people. Regretfully, I put my complete trust in Alan Foster to manage my son's business affairs," LaVar Ball, Lonzo's father, told Shelburne and Lavigne. "At the end of the day, family comes first, and I support Zo wholeheartedly. Together, we will make this right."
Lonzo appears to be distancing himself from the Big Baller Brand, having recently covered up a BBB tattoo on his arm.
Meanwhile, LaVar said the "brand is good," per TMZ Sports, and proclaimed the shoe company will live on beyond the Foster situation.