I had assumed that the word bygone in the phrase “let bygones be bygones” was some sort of insult like saying “let those idiots be idiots…” kind of like “boys will be boys.”

A bygone is actually just something that has already happened. So “let bygones be bygones” means like “let things in the past stay in the past.”

My source also says “LBbB” is similar to “forgive and forget.”