For me the first big lesson was that the body really needs time to recover after training hard, and the second was that training "no matter what" doesn't work if you're trying to improve maximum strength. Lifting is a neuromuscular activity requiring maximum activation, and if I'm very exhausted or sleep deprived, I won't be able to train hard enough to matter, so doing a less intense core workout and lift the next day is more reasonable.
The Bulgarian system of training is built around daily 1-rep maxes, then backing off for work sets.
The nice thing about it is that this means that if you're having a crappy day, you accept it and train what you can. If you're having an awesome day, you squeeze more out of it.
Learning to give-and-take with your "recovery budget" is definitely an important lesson. I train less hard than I'm capable of because my employers don't pay me to be a zombie.