Lil Wayne and Birdman Trying to Squash Beef Privately

Lil Wayne and Birdman's run-in at LIV Nightclub was nothing out of the ordinary, at least for them, because they've been working on burying the hatchet for months ... TMZ has learned.

Sources connected to the former Cash Money duo tell us the $51 million lawsuit between them is still very much on, but they've managed to separate that from their personal relationship. As our source put it, "They're family and that's bigger than money."

We're told they've talked several times over the past few months, and although it's no longer the father-son relationship they used to have, they ARE making an attempt to squash the beef.

As for Sunday night's embrace at LIV -- Wayne had a section reserved downstairs, while Birdman was upstairs. Neither knew the other was there until DJ Stevie J shouted them out.

Birdman's son, Bryan Jr., came down and said "hello" to Weezy first, before Wayne stopped by Birdman's table where they hugged it out.