Was master Zerg, played since BW and even beat some pro players in tournaments, my advice is that don't rely on your mechanics to improve.
I'd say in sc2, you could get to at least diamond without great mechanics, but just knowing what to do, when to do it and how to do it.
I'm sure you are aware in sc2 you need to be doing something every second, and thinking about what you will be doing next, all the time. The same goes in league. Here are Some general tips I can give you that night help:
1) vision wins games, lack of vision loses games, especially in lower ranks. Focus on always warding and always trying to deny enemy vision. You understand how important map control is, get map control early with taking objectives, help other lanes get objectives and establish your map control. Encourage your team to help with vision and always have pinks on the map.
2) prioritize objectives over kills. Low rank players run around trying to get kills because obviously that is the most fun. Objectives are more important because of the map control it gives you. You get bot tower you can then get dragon and put forward wards all over their jungle. You get top tower you control rift scuttler and their top jungle. You get mid and the mid can roam and help other lanes. Objectives are the most important thing, don't dive towers for kills if you can just get the tower without risking your life.
3) lose your lane gracefully. If you are losing lane, just accept it and stop trying to fight and stop putting yourself in dangerous situations to get a few CS, only do it safely. If your lane opponent is slightly ahead, it can be made up for easily, VERY easily, like one gank easily or one team fight, don't let your lane opponent keep killing you, that makes the game way too hard on the rest of the team.
4) as carry roles, CS is undervalued in lower ranks. So much time is wasted roaming around or waiting for fights or trying to start fights that won't happen. Try to aim for 90 CS every 10 minutes, but don't do it mindlessly. Do it where it's safe without over extending and don't ignore your team if you see a fight might happen. Try to ping your team to wait for you to get there, low rank players will die in a fight then blame you for CSing, while higher rank players will know you are farming so they will delay the fight until you are there.
5) if your team is winning team fights, force team fights at objectives like dragon or baron, they have two options: fight you and lose and give you the objective ; or give you the objective. It's a Win/win. If you are losing team fights then try to split up the pressure into multiple lanes. If they are going dragon then get a tower. Wherever their pressure is you can apply opposite pressure. 3-4 man gank in bottom lane? Take mid tower or top tower, wherever the pressure left. If a teammate dies from the gank but you got a tower and a bunch of CS, it's worth it.
6) team compositions can win a game alone, heavy CC dominates lower ranks.
That's all I can think of right now as quick basics. Hope it helps