Since Lando is also appearing in the Han Solo movie, presumably he’ll be the one flying the brand-new Falcon.
In the official Star Wars canon, all we know about Han’s acquisition of the Millennium Falcon was that he won it from Lando Calrissian in a game of sabaac.
Though if this movie is as action-packed as we’re expecting it to be (as one would want from any Star Wars movie), then no doubt the Falcon will take a beating during the story, and as times passes, that paint job will slowly wear away with each new ding and blaster hit.
If I had to guess, Han eventually lost this when he dropped Jabba the Hutt’s shipment to escape being captured by the Empire.