It has been long known that punishment and reward are ineffective for interpersonal influence (e.g., see French and Raven's "The bases of social power" from 1959). Fear is a big factor in children lying. And the nasty side effect of fear is that it leads to repressions of natural inclinations, and eventually a part of the true self becomes suppressed, and a false self becomes a big part of the character. You can see this in the endemic existence of narcissistic character traits in our society.
While studying these topics, the most surprising realization for me was that moral indoctrination teaches children sadistic and masochistic behavior, which then manifests in adulthood as vectors of moral indoctrination towards their children (besides other undesirable behavior in society), and the cycle continues.
Accepting a child for who they are, and not trying to influence them into what the parent wants them to be, goes a long way towards making an honest child.