The dinner-with-Lando scenario makes a lot of sense if you consider the Bespin situation from Vader's perspective. Consider what Vader knows about Han and Chewie. (I'm drawing from the movies only, not all the cartoons and books). Solo is shacked up with the Princess, and has risked his life alongside Luke and the Rebels, but maybe he or his Wookiee can still be bought with promises of money and freedom. One of them might tell me where Luke is! (Then I'll laugh and give Solo to the bounty hunter)
For this to work, I need all of them to at least consider the possibility that I might not kill them all, so I prefer them alive and unruffled (at first). Also, Solo is the promised price to be paid to Boba Fett for his services, so it's best that Solo live. Excessive violence in the facility will also anger Calrisian, who will then become a pest. Keep Calrisian pacified, and he will encourage Solo and the Wookiee to ignore Leia, be smart, and tell me what I want to know. So. Finesse.
I've got it. A nice dinner with their friend Lando. The plan is perfect:
1) They might leave their weapons in their rooms (Chewie came to dinner unarmed).
2) If they take their guns to dinner, I needn't disarm them unless they draw on me, and such force need not be lethal. I'll take care of it personally.
3) Even if I have to disarm them, I will continue to be courteous until I have had a chance to evaluate them. If no sell-outs step forward, fine. That means they're either loyal to Luke, or they simply don't know where he is. Either way, we'll roast them on a spit, and if Luke cares for them, he will come to me. (Then I'll laugh and give Solo to the bounty hunter)
On Jabba's sand skiff, Luke's mechanical hand fully absorbs a blaster shot from one of Jabba's men, and the hand continued to work fine. Vader, meanwhile, did not absorb Han's blaster shots, but rather deflected them with his hand. Is that the force, or an industrial strength mechanical hand? Doesn't matter. Point is, Vader had it handled, and he handled it with finesse.
VADER: "We would be honored if you would join us."
He looks civilized and lawful. These are the deeds that keep businessmen complacent and cooperative toward a tyrannical imperial government, and legitimizes the punishment dealt to those who resist.The movies often focus on Vader's constant reliance on force and intimidation, but the Empire's servants do get paid as well.
Of course we know what happened. Neither Solo nor Chewie would sell out Luke, or the rebellion, and they didn't know where Luke was anyways. Whether they actually sat or ate anything in front of Vader is up for speculation, but they were all in jail when next we see them.