Anyone who calls it quits at 50ms is spoiled, lol. You've got to be consistently above 100ms before you start having issues in this game, and even then a steady connection is often something people can learn to deal with. It's a fluctuating connection that makes people blame their ping.
And yeah, I am acting like latency would be the only problem, because it is. Assume everyone is cranking out 500 APM in a team fight. That comes down to 8 actions per second for each player. You need 4 bits (which can assign numbers 0 to 15) to tell you what player is doing the action, we'll round up and say 8 bits to tell you what action they're doing (spell, items, attack move, etc), and we'll give another 28 bits for where their mouse is (Summoner's Rift is 15,000 units by 15,000 units, which requires 14 bits per direction). That gives you 40 bits per player, or a grand total of 400 bits per second of game data to describe a team fight.
There will be more bits to tell those packets how to get to and from Riot, but in general you'd have to be trying to have a connection so bad you'd lag as a result of bandwidth. Your problem would be patch days, not playing the game.
People have control of one or two connections in their house - their computer to their router, and their router to their modem. Sometimes those are bundled together. But if that's working as good as can be expected, then all the rest of the connection issues would be with the ISP's routers that connect your neighborhood, your city, or your state to the rest of the internet.