I watched a dozen of videos taping the fights between male lions; none of them involve female lions assisting in the fight. It is also known that the male lion who take-over the pride will kill all the under-age lions.
Why don't the female lions help their male lion such that their offspring won't be eliminated?
From an evolutionary perspective, the female lions will surely fight for their children as raising a new child is costly. Though they will most likely not fight to death. Even if a lioness does not have any child yet, her older sisters might already have a child so help defending the entire pride is the optimal strategy. In this case, the younger sister might only contribute half of their strength comparing the older sister, as the child is only her nephew and not her direct offspring.
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 "lion-king" 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.
The prides mostly comprise at least 10 individuals, up to 40 and 1-3 alpha males. The average pride, both in Kruger NP and the Serengeti, consists of 13 members. In Kruger, the average composition of 14 prides totalling 181 lions was 1.7 adult males, 4.5 adult females, 3.8 sub-adults, and 2.8 cubs (including yearlings).
In larger prides, it is rare for the whole pride to be together, but individuals or small groups, typically of three-five members will scatter throughout the pride’s territory for days or weeks at a time, especially in dry environments or times where the number of prey are in small supply.
The mortality rate for the mature males is about 4/1 when they wander in between territories, and when they mount a challenge, it's often as a group of three or four bruising males.
There can be fights of a 270kilo alpha vs 2-3 challengers of 200-250kg, and the question suggests "shouldn't 2vs7 and 3vs8 lion fights happen? to protect the cubs?", including 100-150 kilo females. The females have a very vulnerable neck so a 7v3 serious fight could easily end in the death of 2-3 lions, weak hunts and hunger. That is why they are probably scared to mount a defense.
Animals tend to avoid potentially mortal fights, and the territorial fights are too life-threatening and vicious for the females to risk getting involved in. Prides usually have two alpha males so the strategy of challenges is very dynamic. It's best to find someone who has read a book about social organization of lions.
I’m watching one right now on Disney plus and I was literally wondering the same thing as you until it showed that two out of a pack of 5 male lions initiated a fight and to protect her daughter she charged and fought one of them which inspired the other females and they all started to fight. They don’t show much of the other lion fighting thr prides male but I can assume they did.
I've seen a video or two where the lioness will fight a male to protect the cubs.
And another thing, when a nomadic male or males take over a pride by force, it isn't considered a new pride being formed, it's actual meaning is the pride have new resident males.
Remember a pride is a pride without any males being part of it. Prides are so,
consisting of females only, the males that are there are residents of any said pride. So a pride of lions is so without a male unless they are male cubs of the lionesses within a pride.