On occasion, I have doled out punishment to my son for lying. In particular, he did something wrong and when questioned about this, lied and said he did not do it. Depending on what he did wrong in the first place, he might receive X days of punishment. However, if he lied, he will have 2X more days tacked on.
On at least one occasion, what I considered a punishable offense was reduced when he came to me and 'fessed up before I found out.
I know that my son will not stop incorrect behavior altogether at his age. However, I try to instill in him the lesson that no matter what you did wrong, you only make it worse by further lying.
In Pete Rose's case, I am not going to judge the sincerity of his apology. However, if I ran the show, I would automatically put a 14 year moratorium on his eligibility to the HOF. I figure if it took him that long to finally admit what he did, he should have to wait that long to be eligible.
After the 14 years, depending on his actions, he might be eligible for the HOF for his on field exploits, the message being that not only are you expected to come clean, you are expected to do it expeditiously.