Why don't the female lions in a pride help their male lion to protect their children from other males?
Alright, after watching a few more documentaries, here is what I found:
Lionesses do try to expel nomadic males, even if the male lion is not in presence.  On the other hand, I am still yet to find a single video taping the male and females collaborating to expel the invading lions.
When invading a pride's territory, the nomadic brothers will usually not attack first, even if there is only one &quot;lion-king&quot; in the pride. The nomadic brothers might think that the females will help the lion-king to protect the territory; otherwise the brothers will just simply attack as it is a 2 to 1 odd.
The nomadic brothers will usually disrupt the pride's food-supply first. As the pride usually have many cubs to feed, it consumes much more food than the nomadic brothers, and the lion-king is then forced to launch his attack first.
The fight between male lions are usually not lethal possibly due to male lions' body structure. Most of time the nomadic brothers are expelled, but sometimes the lion-king is wounded or expelled from his own territory.
After being wounded, the lion-king cannot protect his cubs. The nomadic brothers then start to find and kill the cubs. The females do sometimes try to protect their cubs, but their attacks can only lightly wound the male lions as males are well-protected by their hairs. In contrary, the males can one-hit the youngsters.
Cubs close to 2-year-old do try to run away and the females do sometimes help them by providing them food, even if the females seem to be obedient to the new dominating males. In this video the lioness even decide to run away from the original territory to raise-up her children and half-children: https://www.youtube.com/watch?v=eMgPf83uDec.
After all cubs are killed or expelled, the females lose the motivation to fight against the invaders, and the new pride is formed.