If people don't respond, deflect or lie, I would stop engaging with such people.

IF it is important stuff you need from specific people, I would be direct: 'I need this response for [whatever purpose] and I am waiting on you to get back to me'. So tell them explicitly you are waiting on them for X or they didn't get back to you about X.

For such people, it would be best to be clear and direct rather than asking them the same thing repeatedly. I would also avoid dealing with these people if at all possible (unless unavoidable)