The question is highly hypothetical and trying to write an answer is tiresome. It is irritating but judging by the hundreds of thousands of words written on this topic, people are interested in it. The question is hypothetical because, although I am a good searcher of information on the Internet, I can’t find a single recorded example of a healthy male lion genuinely fighting a silverback gorilla. Despite the unpleasantness of such a fight, it would have been nice to have such a record upon which we could begin to write an answer to the question.

All the discussions are based upon the bite force of these two animals, their speed, their strength and their intelligence et cetera. But these factors are not the complete picture. Of course, too, there is aggressiveness and a willingness to fight which must be a factor. However, at the end of the day no matter how much science you apply to composing an answer, it comes down to guesswork. The two never meet. Lions live on the wide open, arid plains of Africa and gorillas live in forests up in the hills.
The most high-profile meeting of a big cat and a gorilla occurred in a well-known encounter in Spokane, Washington, at an animal show (reported 23 September 1949 by the Virginia Chronicle – see report at base of article). The fight took place in a cage. The 312-pound gorilla’s behaviour was entirely defensive when attacked by a 185-pounds black panther. The size of the cat indicates that it was a melanistic jaguar. This is the third largest cat after the tiger, being the biggest, and the lion the second biggest. And so, the encounter has some relevance to answering the question but it seems to me that the gorilla was not prepared to fight.

The gorilla may have been quite tame and passive. They are intelligent and being captive they may have formed relationships with the keepers or learned to become less aggressive. Judging by the report, it seems that the gorilla was surprised by the attack. The jaguar did not kill the gorilla but severely harmed him and attendants apparently euthanised or killed the gorilla out of mercy. The panther had torn the arm off the gorilla and inflicted other painful wounds. We don’t know whether the story is accurate or even truthful. But I would argue it doesn’t help us in the slightest because we don’t know the mentality of the primate. Clearly the jaguar was in a very aggressive mood for some reason or other.
Having read a number of articles or posts by people who consider themselves to be expert on this matter, but who are laypeople without qualifications or recognised expertise, the consensus is that the lion would win in a lion versus gorilla fight perhaps mainly because of their speed and predatory instincts.
After all, gorillas are non-carnivorous. They are herbivores. They are not predators and the predator has a skill set which makes them very good at killing. Their mentality is geared up to killing. That’s why, I guess, the story mentioned above suggests the gorilla was very passive and defensive.
It is likely that this critical difference in mentality would give the lion an overriding advantage if a fight should ever be commenced between a gorilla and a lion.
However, even if these two impressive animals did live in the same area i.e. they were sympatric, they would avoid each other. Certainly, a gorilla would avoid an adult male lion and a lion would probably avoid adult male gorillas in the interests of self-preservation. It’s just not worth the risk of injury to tackle a silverback gorilla. An injured lion is going to die of starvation probably.
Apparently, there are records of leopards (much smaller than a lion) attacking gorillas but no doubt these were sub-adult or young gorillas and/or sick gorillas. But the question is about a fight between a healthy male lion and a healthy silverback gorilla. It ain’t going to happen, it has not happened and to speculate on an outcome is a waste of time. And the videos available online on this topic are all sensationalised and fabricated. They are horrible.
The text of the media report from 1949:
“SPOKANE, WASH.—It was generally agreed that Barangtu, a 312pound gorilla, never had a chance in his two-hour death struggle with a snarling 185-pound black panther. Zoo authorities and the owner of the two animals expressed the opinion that despite the weight advantage, Barangtu was fighting far out of his class. In fact, according to witnesses, the gorilla passed the entire two hours seeking to ward off the savage onslaughts of the enraged panther. More than 400 persons were virtually hypnotized by the death struggle in a cage at # a Liberty Lake animal show. When the battle was ended, the gorilla lay dead, mercifully murdered by show attendants. Before the attendants shot Barangtu, the panther had torn his arm off and inflicted numerous painful wounds. “
Below are some more articles on lions.