itsa TEAM game. I'm stuck in silver 4 too and yes this is mostly because my jungler doesnt want to gank a 'random'/non premade lane or becuase one lane decides to int like shit. But its still a team game, when one champ is fed or one of your mates doenst do good its your teams job to deal with it. I know it can be super frastrating but theres no way around it.
Personal LP only works til a limit. I think it's important, even neccessary to give LP based on your very own perfomance, on the other hand you should use LP when losing, because its a ranked system it has to work like this.
Example: I once had a game with a Yasuo in my team who feed the enemy toplaner like shit. It was insane. Around minute 20 he was 0/11/2. It wasnt going good,even though all the other lanes were doing quite even, teamfights were always a 4v5 and we couldnt contest objectives. Nonetheless this Yasuo did his job, everyone was flaming him to a point were I personally would've jsut afk tbh. But Yasuo just splitpushed wherever he could, baited out their ults and pressured them on the sidelines so we had the change to win 4v4 or even 4v3. He pushed the base all by himself and won the game almost singlehandedly. He went 1/19/2. Judging his Kda he shouldnt get many LP right? And thats were the system would be kind of lacking.