Lag spikes ruining the game at critical moments

I've been playing Tahm Kench support for the past couple of days and every time I need to devour a teammate to save them or a gank is happening, or a teamfight breaks out, I start lagging. Often, this will lose us the fight or give the advantage to the enemy team which leads to us losing. My internet or computer isn't the problem, and I've heard it happening to others to. Please fix this so I can play a match without feeling like I'm inevitably going to give the game to the other team because of something out of my control.