A Shared Problem

I have had this problem for around a month long, and it is increasingly getting worse. Upon a game starting (spawning at the platform) I start out with no lag at all then very quickly it gets worse until I can't cs or clear jungle camps, much less fight an enemy champion. I have discussed with several other players I know, including a plat player (I'm silver although this doesn't have much to do with the post) and we have determined that the only way to prevent this lag is that...

-the moment you spawn you use task manager to force close league and the client -then restart and reconnect to the game. After we do this, we have no lag issues the rest of the game. Several times my teammates have gotten angry with me, but its the only way I can fix the issue. Is this an issue with the game? It seems to have started after a recent update, although I cant recall which. The reason this is a major problem is I often miss the first wave or two of minions (and so a level and some gold behind) and this completely ruins any chance I have to help my team to invade or protect from invades. It subtracts heavily from game play and we have no known fix.

Any suggestions?