British Army bomb disposal units in Iraq and Afghanistan did not receive training in Lean, Six Sigma, or any other process improvement methodology. However, they continuously improved their processes and equipment, often on an hourly basis. The lack in improvement methodology was more than compensated for by a very active continuous improvement mindset and extreme levels of delegation.
This need for continuous improvement was driven by the knowledge that the enemy (eg Jaysh al-Mahdi, Al-Qaeda, the Taliban) were always watching what we did and improving their tactics (processes) and bombs (equipment) to defeat us. Quite literally, if we couldn’t iterate improvements faster than the enemy, people would probably die.