FSG doesn't just own the Red Sox. They also own Liverpool FC and the Roush Fenway NASCAR team.
Which is how LeBron got in with FSG he's been a minority owner of Liverpool for years. They're probably looking towards an expansion into basketball sooner rather than later and Bron is the perfect guy to partner with in that regard. Bron said he wanted to be an owner, he's got a vehicle now. Man's making boss moves to the king.