Matt Berry hammering through one of Military Athlete's Lab Rat sessions. This session had 96 one arm snatches @ 24kg along with plenty of other nasty shit. Our Athletes finished in 14-20 minutes. Best thing about this session was the exercises were super metabolic and the loads were heavy so it was a great circuit for training mental toughness.
Mental toughness can and should be trained in the gym environment.
Funny thing about mental toughness is that it is mode specific. I remember seeing an elite Crossfit Gym owner getting destroyed in an olympic distance triathlon, while two of my training partners who were former triathletes rolled though it easily 45 minutes faster.
Fitness is mode specific. There is no cure all.
Your goals should dictate your training.