{WARNING: contains some spoilers from the "New Young Han Solo Adventures" series written by Ann Crispin.}
Lando Calrissian first met Han Solo on Nal Hutta, when he saved the smuggler from the notorious bounty hunter Boba Fett. Lando had recently acquired a new ship, the Millennium Falcon, on his journeys, and had heard of Han's reputation as one of the best pilots in the business. It's just fortunate for Han that Lando showed up when he did. But not satisfied at stopping Fett, Lando turned the hunter's own weapons--mind controlling poisons--against Fett, humiliating him soundly. Highly grateful, Han taught Lando just about everything he knew about piloting, although he swore to himself from the start that he'd one day own the ship he fell in love with the moment he entered it.
Han and Lando had a working friendship, partnership, and occasioanal friendly rivalry for years. They occasionally drove each other insane or had a minor "battle" over a woman, but in the end they were close friends--for some time Lando probably was the closest human friend Han had, the closest of course being the Wookiee Chewbacca. They often made smuggling runs together, and just ran into each other throughout the Galaxy. When Lando opened a shipyard, he leased Han his first "real" ship, which Han named the Bria, after an old love.
Lando took part in the Battle of Nar Shadda, then moved on to a professional life as a gambler instead of a smuggler for some time, taking "respectable" businesses on the side off and on for years. He ran into Han again in a high-stakes Sabaac match at one of the galaxy's biggest sabaac tournaments. The two made it to the final round, Lando on his skill as a gambler and Han on mostly pure luck. Lando, running low on credits, offered a "marker good for any ship on (his) lot," instead of dropping out. Han managed to win the game, and claimed the Falcon on a technicality--although the Falcon was Lando's personal ship, he'd taken a luxury liner to the tourny, for the sake of making an impression, and left the Falcon back at his shipyard. Lando was upset at Han for this, but eventually forgave his friend, mostly because he, being a man who enjoyed classy things, wanted a classier ship the beat-up Falcon. Very shortly after losing the Falcon to Han, he ran into Bria and wound up saving her from Fett as well. Fett grew to truly hate Lando.
Han and Lando did have a huge falling-out, but it was NOT about the Falcon, as many believe. Han was recruited by Bria, now the leader of a rebel cell, to hire all of his smuggler contacts to help them on a raid of the hutt-controlled slave-planet Ylesia. The smugglers were promised a share of the profits, but Bria had gotten special orders, demanding she take all the money for the Alliance. She betrayed Han in the process, but Lando and most of the other smugglers believed he had double-crossed THEM. Lando left in a rage, seeing Han only once in many years until they met again at Cloud City, Lando's newest "toy" and "respectable" business. Even then Han was met with old bitterness. "You've got a lot of guts, coming here after what you pulled."
But after he was betrayed and double-crossed by Darth Vader, Lando realized he couldn't hate Han as much as to leave him in the hands of a Sith lord and a truly irate Hutt. He had a change of heart, and made for Tattoine, where he disguised himself as a guard in Jabba's palace, making sure he was positioned on the Skiff where Luke, Chewie, and Han were to be fed to the almighty Sarlaac. Although it turned out Luke had fewer in the ways of "delusions of grandeur" than everyone thought, Lando was in an excellent place to lend a much-needed helping hand to the company.
Lando then signed on with the Alliance, was given the title of general, and flew the Falcon on the attack on the second Death Star, nearly dying inside it in an explosion of flames, but showed his true ability as a pilot and just barely outran the fire. After the war was over, he returned to civilian life.
He got his hands in just about everything again, taking part in things from a mining operation to a funhouse. He "settled down" as it were, meeting and finally marrying Tendra Risant and they worked on yet another mining operation on Destrillion and Dubrillion. But anytime war threatens and the Alliance really needs his help, he's well-known to come out of "retirement" and help out again.