The basic precepts of Buddhism, not killing, not stealing and so on, are very important aspects of Morality. You can't get away from the fact that we define Morality as to how we act and how we speak. So if we are lying, that's not good speech, if we are killing, that's not good bodily actions. Since Morality is explained in that way, I don't know if there is anything more important than simply trying to follow those principles.
Now, we don't teach the Five Precepts. We teach what is underneath them. They all come out of Compassionate Understanding, Compassion and Lovingkindness, being kind, being friendly to others, considering others' well being. We stress and teach all of you, how to develop this Compassionate Intention. So we don't feel we have to teach the Five Precepts as they are, because if you develop what we are teaching, you will automatically follow the Five Precepts.
So if a person is looking for something underneath the Morality, as to what actually makes it work, then we could say the Compassionate Intention, that's what's below it. Now in that sense, Truthfulness and Morality would go together if we are very true to our direction to be more compassionate and kind.
The little bit at the end of the question, about respecting laws of nature, opens up the Wisdom part of our practice. To actually understand the laws of nature is part of our Wisdom side.