Your view of the roles undertaken by lions (males) and lionesses (females) in the nurturing and rearing of lion cubs seems to be a reversal of the realities.
Lion cubs stay with their mothers and under mothers' protection and nurture for about 2-3 years. When a pregnant lioness nears the time she's to give birth, she leaves the pride and goes to a safe, secluded place like a nest of bushes, a sheltered ravine or a cave. There she will give birth, usually to one to four cubs. Because the cubs are tiny and defenseless, the lioness will remain with her cubs away from the rest of the pride for the first 6 weeks or so of the new cubs' lives.
One of the groups that female lions guard and protect newborn lion cubs from are adult male lions, including ones in their own pride. And including the newborn lion cubs' father.
Once the baby lions are old enough, the mother brings them to the pride. In a pride, the adult lionesses who've borne offspring raise their cubs collectively, forming creches where all the lion mothers pitch in to take care of their own and each others' cubs and help each other out. Whilst raising cubs, lion mothers perform many tasks which include nurturing, guarding, teaching and playing with their own and other lioness' cubs along with other standard lioness jobs such as hunting and patrolling and keeping an eye out for interlopers and dangers in order to protect the pride.
As cubs grow up, mothers and other female lionesses will continue to need to protect them from older cubs of both sexes who tend to be bullies, and often from various adult male members of the pride too.
Like infant humans, baby lions can't eat meat or other solids when newborn, in part because they are born without teeth. Lion cubs start growing baby teeth or "milk teeth" soon after birth, and when they are about 3 months old they begin eating little bits of meat.
From birth until they're old enough to live entirely from eating meat, lion cubs are kept alive and thriving by drinking the milk made by their mothers and other adult female members of the same pride. This involves suckling the teats of their mothers and other female relatives. Lion cubs suckle like this several times a day every day until weaning begins at age 6-9 months. The human equivalent is breastfeeding.
Lion fathers cannot and do not lactate and feed their young "mother's milk" from their bodies. Lactation and all the nuzzling, cuddling, snoozing together and other mother-child bonding that goes along with suckling are essential nurturing activities that male lions cannot and do not perform.
Yes, some adult male lions do play with, snuggle and nurture cubs.. But it's not true as you have suggested that the lion's share (LOL) of nurturing cubs is performed by male lions whilst female lions spend the bulk of their time doing guard duty instead of cub care.
Female cubs will remain with the pride they are born into for the rest of their lives. But when male cubs reach age 2-3 years, they get kicked out of the pride. This job of kicking them out is left to the adult members of the pride, including their fathers.
I would describe the roles that female and male lions play in the rearing of lion cubs as sex roles, not gender roles. In my view, sex describes the means by which millions of different plant and animal species reproduce and insure that species are perpetuated, whilst gender refers to roles, customs and stereotypes that are associated with humans of the two sexes that sometimes might be, or seem, related to sex and the perpetuation of our species, but which are not essential to it.
Sex in my view means male/female. Sex is a matter of biology, nature and material reality, and it's binary. By contrast, gender is masculine/feminine.
Gender is a set of narrow, confining ideas that different cultures have created about the roles, modes of dress, ways of grooming, behaviors, interests and personality traits which each culture associates with, and sees as appropriate for, boys/men and girls/women at a particular point in history. Whereas sex is binary, gender - like height, weight, body shape, hairiness, vocal pitch, etc - occurs across a wide spectrum amongst the human population, with considerable overlap between the two sexes.
Most human babies, children and adults have personalities and personal styles that contain a mix of elements that could be seen as masculine or feminine by the standards of one's own or another culture. But with the vanishingly rare exception of some individuals with a small handful of DSD conditions, all of us can very easily be categorized as either male or female - and others can tell our sex at first glance.
I think gender is a human construction, not something that other animal species engage in. IMO, lions behave the way they do when mating and rearing their young because of sex, a matter of nature affecting myriad animal and plant species. Not because of gender, a matter of culture created by humans that I'm wary about projecting onto other animals.
At any rate, the way you describe the supposed "gender roles" of male and female lions in rearing offspring sounds to me more like what happens with the fictional elephant who heroically steps in when the the flighty, lazy mama bird Mayzie abandons her offspring in the Seuss classic, Horton Hatches the Egg, than what actually happens amongst RL lions in the wild