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Nowhere in the film does Vader ever indicate that the Empire will take over the city, nor does Vader even seem interested in anything outside of Luke, and to a lesser degree Leia, Solo, and Chewbacca.
Lando only tells his people to evacuate after betraying the Empire, which would seem to indicate the city was safe until then:
Further, Leia and Chewbacca didn't even understand Lando's motivation when he freed them.
As such, what was his actual motivation for abandoning Cloud City?
You have to consider the timeline, the way the deal is changed through the course of the film, and his reasons why.
When the Imperials first arrive at Bespin, he is trying to protect his interests as he says to Leia when she asks him about his fears of Imperial interference.
"I've just made a deal that will keep the Empire out of here forever."
At that point, he believes the deal is simply to allow the Empire to capture Skywalker while Han, Leia, and the rest will go free.
They then understand that Vader is there and what the deal is, at that point Vader tortures Solo, something he had not told Lando about. As Lando explains to Leia, they just want to get Luke.
Then the deal changes again, with Han being frozen in Carbonite and handed over to Boba Fett, and Vader decreeing that Leia and Chewbacca be kept on Cloud City
Lando demonstrates the deal is getting out of his control when he says
"This deal is getting worse all the time."
and Vader
"I have altered the deal. Pray I don't alter it further".
Finally, a 3rd change is made with Chewbacca and Leia being taken out of Cloud City and Vader deciding to leave a garrison.
By this time, Lando realises that he has lost all control of the deal and more than likely he and his people will be arrested, enslaved, or worse by Imperial forces. He decides then to fight the Empire and escape rather than wait until it is too late to be able to do anything.
It has been suggested that he is more worried about earning money than his people, however if that where the case, he would have left quietly and not given a message informing his people to escape. In addition, this idea does not match with the character as he has been portrayed throughout the Star Wars Universe.
"Our operation is small enough not to be noticed. Which is advantageous for everybody since our customers are anxious to avoid attracting attention to themselves."
This does not necessarily mean he is trading with evil criminals. He could be providing supplies to anyone that the Empire does not want to have access to the resources of Bespin: rebel groups or organisations trying to supply planets being cut off by the Empire; he could well provide services that are relatively cheap for the risks involved. It would have been easier and possibly more lucrative to open his doors to the Empire and, in the same way as the Hutts, enter into an agreement with the Empire them turning a blind eye.
There is another suggestion that Lando needed to get forces in place in order to betray the Empire: he needed to buy time so repairs could be made to the Falcon and ensure that when the time came to fight back, everything was in place to do that successfully. There is no clear evidence for that other than some sources online that suggest Lando was already involved in the rebellion. These may or may not be canon, so I won't add them as fact here.
One of the things that Vader was threatening was to to station a garrison, effectively turning the residents of the station into slaves and the administrators (including Lando) into puppets:
VADER: Good. It would be unfortunate if I had to leave a garrison here.
Lando subsequently discovers that his security codes have been changed, which shows that he's no longer in charge of the city:
[Chewie returns their fire as Lando punches desperately at the door's control panel.]
LANDO: The security [code] has been changed!
He (rightly) assumes that the Empire isn't just going to leave when Vader's done and decides that the only option is to flee the city. He also encourages the residents to do the same.
Interestingly, the Official Fact File #6 for Lando indicates that he was a) Already aligned with the Rebellion and covertly offering them assistance and b) that his key decision to double-cross Vader was because his conscience got the better of him.
Lando's betrayal of Han troubled his conscience, which got the better of him when Vader went back on their deal. Lando offered his assistance to Leia and the Wookiee (hewbacca, whose
In your own answer, you write that Cloud City is neutral. You may think that, and Lando may have thought that initially, but the Empire on the other hand surely didn't! The Empire has the claim to consist of all of the (known) galaxy far away after all, even if it does not always enforce that claim. This is mostly a pragmatic decision: It's expensive to have a garrison on every little piece of rock (or gas, in this case) in the galaxy. Especially since the Empire is still relatively young (about two decades) and by far not yet done with establishing full control over much bigger and much more important planets (see Alderaan for example, or the whole Rebellion for that matter). For the time being, if a planet does not support the Rebellion, the Empire is fine with a little autonomy as long as the planet is loyal when needed.
Compare the situation on Tatooine. It wasn't even really part of the Old Republic (maybe in name only), but still when the Imperials land there in Episode IV, they sure act like they completely own the place. Presumably, the Hutts have made a similar deal like Vader and Lando's.
Unlike Tatooine, Cloud City is a lot less populated unfortunately. Leaving any real garrison on the former would actually be quite a task, but on the latter? The only real reason there wasn't one yet is that it was just not that far up the Empire's priority list so far. But also unfortunately, Cloud City has shot up that list since high profile rebels have tried to seek shelter there. It's not unreasonable to assume that Vader will want to leave a few dozen stormtroopers to make sure that Cloud City will remain rebel-free and "in line".
Lando initially thinks that he can prevent that (and save at least some of Vader's targets) with his deal. In his naivety (pride), he acts like he is an equal to Vader! But he isn't, and Vader makes sure to drive home that point basically any time they meet, by showing that the deal is absolutely meaningless to him. It takes a while for Lando to realize how powerless and at Vader's mercy he is. At that point, it's either betrayal or becoming a puppet (and by acting somewhat defiant to the amendments of the deal, Lando can expect some extra supervision, or even the "you have outlived your usefulness" treatment).
And indeed, picking betrayal turned out really well in the end.
When the Imperials first arrive at Bespin, he is trying to protect his interests as he says to Leia when she asks him about his fears of Imperial interference.
Lando was also trying to protect the people of Bespin. Why else would he warn the citizens that the Empire was taking over before he left with Leia and Chewie aboard the Falcon?
