As for lying, we set that down in stone, big time. When my son lied to me, after I proved that he had lied, I spanked him with a belt on his bare behind. That caught his attention!
We also explained to them that no matter what kind of trouble they ever got into, as long as the TOLD THE TRUTH, we would help them resolve the problem.
That's the wy we parents were raised.
I burned up my Dad's 6 month old Chrysler 300 by going 130+ mph (electrical fire). He asked me what I was doing, I told him the truth, and heard nothing more of it.
[We also explained to them that no matter what kind of trouble they ever got into, as long as the TOLD THE TRUTH, we would help them resolve the problem.]
You sound just like my parents (whom I respect GREATLY) and this is exactly the way I try to raise my daughter.