Lobot's story in the Star Wars universe had been a mystery for a long time before the Lando comic series came out in 2015. And to a certain extent, so had the story of Lando Calrissian. But, Solo: A Star Wars Story has shed some more light into the life of Lando, which highlights his pansexual and fluid lifestyle in certain scenes. Donald Glover, who plays the young Lando, along with screenwriters Lawrence and Jonathan Kasdan have confirmed this aspect of Lando's personality, which brings up the question of whether or not he and Lobot were lovers in The Empire Strikes Back.
Empire Strikes Back didn't really paint a clear picture of Lobot. He lived in Cloud City with Lando and was a member of his security team, but that was about it. We never got any explanation of his mysterious headband or the true relationship between him and Lando. It wasn't until much later that we learned his headband is actually implants placed there by the Empire when he used to work for them. As it turns out, he is always fighting the headband from fully taking over his brain, ever since he defected from the Empire to work with the pansexual Lando, who has been given the recent nickname Pando.
In the 2015 Lando comic series, it's revealed that Lobot and Lando are very close, almost like brothers. Lobot is the brains of the operation and the heart and conscience, while Lando is the gambler and the charm. The two finish each other's sentences in the comic series that ran from July through October of 2015 and are very close up until the very end. While this doesn't come across as them having a sexual relationship on the surface, Solo has given more insight into the ways that Lando operates.
In Solo it is insinuated that Lando and his droid L3-37 could have had a sexual relationship. L3-37 tells Qi'ra that their relationship is complicated, much like that of the one between Han Solo and Qi'ra. L3-37 reassures Qi'ra that "it" works, leaving the female human to be puzzled for a moment. There are many aliens, droids, humans, and other things that Lando has no problem hooking up with, so why not one of his best friends and most trusted allies? L3-37 is more of an outspoken voice in Solo, but she fits nearly the same role that Lobot will in the future for Lando.
Midway through the Lando comic series, Lobot is stabbed by an Imperial guard and badly injured, leaving Lando to put him in a bacta tank before his implants fully take over his mind. In the end, Lobot doesn't make it and the headband fully takes over, but not before he leaves Lando a touching note, urging him to get out of the game while he still can. Lando vows to find a cure, but it isn't clear if he ever does, much like he vows to put L3-37 back together in Solo. There are many parallels between L3-37 and Lobot, which Lando obviously picks up on when they meet later in life. It's not entirely out of the question that the two could have had a secret affair during the events of Empire Strikes Back. You can purchase the Lando comic series over at Marvel.