Champions not showing up on screen + lag

My ping and internet is fine; but, I'm having consistent lag, horrible ability delays, AND enemy champions aren't showing up on my screen. All of a sudden, they will pop up on top of me and my health bar disappears. Abilities will go off a few seconds after I tell them to... This happens with some games, not all. It results in me losing, most of the time, making the game unplayable.