It ain't even original according to this site:
Update! An anonymous commenter correctly pointed out that Kevin Garnett dubbed the Celtics "The Ceatles" back in 2007 -- "We're the Ceatles...Ceatles...like the Beatles? We the Ceatles. And I'm Paul!" -- so LeBron wasn't even being original.
Another update! A different anonymous commenter directed me to The Heat Index, which provided a link to this Tweet from SI.com's Chris Mannix:
Here's why LBJ's "Heatles" line rang a bell. In '06 Drew Gooden told me DG, LBJ & Damon Jones called themselves "The Cleatles." Not kidding.