The "Me, Myself & I" rapper and singer were leaving Avenue Tuesday night in L.A. ... showing all the signs of a new couple. It was the third night in a row they'd been out and about together.

Eazy and Lana started the turn-up Sunday ... leaving Warwick together. Monday night they were at Beauty and Essex. Not to mention ... they were kicking it at Coachella too.

So, yeah ... they're connected at the hip now.