Lil Wayne and Birdman Back Together on a Track ... for Love of 'Hate'

It's #TBT for Birdman and Lil Wayne ... who got together to make music for the first time since their cold war broke out.

The Cash Money/Young Money honchos both dropped verses for Mannie Fresh's new cut, "Hate" -- which also features Juvenile.

We're told they were NOT in studio together for the recording -- Wayne laid down his part more than a year ago, and Birdman did his a few days ago -- still, it's another sign they could be closer to ending their feud.

They've partied a few times since New Year's, and Birdman publicly vowed he'd die for Weezy. But as we've reported ... Wayne is standing firm on his financial demands.

Next step -- "Tha Carter V"? Please.