Imagine having a business process where 3 inputs are required. In the worst case the bot has to ask 3 questions and in the best case the user gives us all required information in his/her first message.
Is it possible to build those kind of conversation flows in the luis.ai interface (similar to Amazon Lex) or does it have to be hard coded?
No, this is not possible in LUIS if you are using Bot Framework proper. LUIS simply does the intent and entity recognition and cannot, on its own, drive a dialog flow.
I don't have a lot of personal experience with it, but Power Virtual Agents may be able to do what you want. There is some information here. It is certainly possible to code it as well, though I know that isn't what you were asking. You just check on the step if entity exists, if so go to the next step, if not prompt the user. Managing your variables at each step can get a bit tricky this way though, as you do not want to assign stepContext.value to something if you skipped the prompt.