Not fulfilling a promise build distrust, but ultimately it depends on multiple factors to determine if an unkept promise is a lie.
A promise can be made using incomete knowledge of all the variables, and further down the road as you get a clearer picture you realize this promise cannot be kept.
The intention behind the promise, and how transparent you are about the possible outcome is important between failing to keep your promise and outright lying about it by keeping everyone in the dark as long as possible (to the benefit of the person who made that promise and to the detriment of everyone else).