For reasons unexplained in ESB, Lando seems to have a disdain for 3P0 from the moment they meet. Let's take a look at the evidence: - Lando gives 3P0 the cold shoulder when he tries to introduce himself on the landing platform. - 3P0 is blasted to bits by an unknown Cloud City resident (hit set up by Lando?). I am sure the old EU named the character that destroyed 3P0 and gave him a novel duology, but he is unnamed and unseen in the film. - The ugnauts attempt to melt down C3P0's dismembered limbs (attempted coverup ordered by Lando?) - Lando makes a snarky comment when he see's 3P0's severed limbs and decapitated head sitting on the table in Han and Leia's quarters. Maybe he was upset that his plan to destroy 3P0 and cover his tracks failed? These actions by are evidence of a deeply held bias against the droid by Lando. But why? Is it simple bigotry? Even when only considering the classic trilogy there is evidence that droids were abused and viewed as subservient by many sentient organic beings. Regardless, it is never made clear in the film why Lando acted the way he did towards 3P0.
I think Lando was just really interested in Leia and C3PO was just a third wheel he ignored. Plus in the GFFA, droids are often treated rather poorly. I always assumed C3PO stumpled upon a squad of stormtroopers who shot him to silence him. It seems melting down C3PO was part of a coverup so as not to tip off the heros. If Lando ordered it, it would have been under duress from Vader, if not Vader or another imperial had made the order. Likely the stormtroopers just disposed of C3POs parts into a trash chute. Lando was likely upset because he is under duress from Vader and worried about what will happen to his people if Vader gets mad if his plan goes off course. Vader has a very bad temper and likely would take his anger out on Lando or the people of Bespin if things do not go his way. Not to mention he was screwing Lando over and over with his changes to their deal.
Lando gave 3PO the could shoulder on the landing platform, because he was mesmerized by Leia. It wasn't a hit set up by Lando. I have never heard this anywhere. 3PO was simply in the wrong place at the wrong time and got blasted, presumably by a stormtrooper. Lando wasn't aware that the ugnauts were trying to meltdown 3PO, evidenced by his confusion when he finds 3PO dismembered.
C-3PO was blasted by a stormtrooper. This is evident when he finally got back online and went, "Stormtroopers? Here? I must warn the others! Oh no! I've been shot!!" Lando had no clue what was going on with the droid as he was too distracted with the bigger problem of Vader holding his city and people hostage.
I agree with the others that Lando was only interesting in Leia and would have cared less about anyone that stood in his way, droid or organic lifeform. It is telling in the Star Wars ESB that Bespin society treats the ugnauts as second class citizens and for fun they toss around the head of C-3PO. A well respected workforce with Labour rights put first would not be enjoying so much free time on the job.
