You don't explicitly say, but I'm going to assume that you want a human society. Some of this becomes easier in an alien society, as we don't have to work around actual human behavior.
NOBODY will accept the fate that he is inferior than the others and just die, ESPECIALLY when he is "intelligent"!
Sure, so the society won't operate that way.
Instead, there will be a constant proffer of hope that some day, the currently inferior will prove himself and gain a mate. By the time that he realizes that he never will prove himself, he is over the hill.
The initial claim will be that they are too young. And some will graduate from that to become head of a pride. But others will be just a bit weaker or slower. They will always be behind the best of their age. Some might be enough smarter or have the ability to learn to be better such that they can compete later in life.
Such a society might have a competition culture, where most lose but all think that they can win. Perhaps the competition is kept always close. So even the weakest and dumbest think that they are just a step away. Individuals may spend large parts of the year training for the competitions.
The females in a pride may support one candidate over the others and give preferential treatment, adding a political component to the contests.
And the long period of "lacking female companion" (plus jealousy and envy) will definitely twist your mind and commit unspeakable crimes such as rape or murder.
Well, the lion solution is that if you murder one of the lucky few, you become one of the lucky few. I.e. a male leader of a pride may lose a challenge to a nomadic male, who then becomes the leader of the pride. That might last a long time in a society like this.
Rape is more complicated. Lions have an estrous period where they strongly want to mate and do not have sex outside it. It is unclear if they would ever consider themselves to have been raped. I.e. rape may not be a meaningful term to an estrous species. Sex is more like scratching an itch than an activity pleasurable in its own right. Humans of course work differently.
Note that male lions are greatly outnumbered by female lions in a pride. With humans, the females might gang up together and kill an abusive male. It's unclear what would be considered normal in such a society and what would be considered over the line. But a male attacking a lone female would be rare, as females travel in prides. It's only the males that travel alone or in small groups.
It is also possible that this society would have more bisexual members. Young males might band together for companionship and sex. Later, they might "graduate" from that to a pride. Some may prefer the companionship of other men throughout. This may be described as a spectrum of sexuality, ranging from only mates with females to only mates with males. Same sex sexual activity has precedent both in humans and in lions.
An individual male who is sexually aggressive, only interested in females, and unable to find a pride might be subject to destruction or imprisonment. Or simply may be barred from the competitive events that allow one to find a pride after breaking the rules in some way.
Males may also sublimate their sexual desire in other activities. Or masturbate.
One reason that people would join the Catholic church was so as to remove the threat to their relatives. Because priests and monks do not marry, they can't have (legitimate) kids. So they are not a threat to their siblings' dynastic hopes. This made the church a useful place to send younger noble children. They would find alternative ways to compete, possibly advising their brothers or nephews. Or they might compete in knowledge. When those with knowledge but not muscle would be allowed to reproduce would be a major step toward civilization in that society.
The first step might be a particularly strong male giving his castoffs to his brother. If someone tried to challenge the weaker brother, perhaps the stronger would fight his challenge for him.
Another option is castration. Perhaps anyone can challenge, but if the challenge fails, the challenger is castrated. This could be brought forward around the same time that the knowledgeable started being allowed prides. Prior to that, the loser might always be killed. In that circumstance, castration might be the more merciful alternative. But as civilization develops, it will become the primitive remnant, as some see capital punishment and imprisonment now.
Both death and castration make challenges risky. So rather than challenging constantly in the hope that you might get lucky, you prepare for one single challenge. But the hope remains.
This allows for competitions based in something other than physical combat that still have serious consequences. Yet another alternative would be to simply give each and every male one chance at a challenge.