Lan's determination was indeed commendable.
The fully armored young woman not only has determination but also has the courage to fulfill that determination. That cold murderous intent that could make people freeze demonstrated that she had experienced the mountain-of-corpse-and-sea-of-blood kind of trial, absolutely not just boasting about it. Nowadays, the Gray Mountain has been in decline, leaving she alone. Yet, she was actually able to prop up this Gray Mountain. This meant that her strength was not to be underestimated.