Trustworthy, sincere, reliable are the right words. I believe that everybody wants to have relationships with the people of such qualities. So, everybody should cultivate these features himself / herself and then they can expect the same from others.
As for me, I don't stop relationship with the person who told me a lie once. I always give one more chance to people, but I let them know that I don't like this. Then people take into account my attitude towards the liars and don't try again to cheat me, or became very careful and even creative.
For example, all my students know that it is better to tell me that he or she is not ready today before the lesson starts than I'll catch someone when the lesson is underway. All my students know that if they work hard during the semester, they will have exellent marks automatically even if it is the whole group and I won't cheat them - so it will be. All these are my life principles or someone can call it 'morality'.