Explain to them that you really enjoy playing League of Legends - you get to interact with other people and you enjoy the competition. However, because of the way the match runs (you may need to exlpain a little how the game works - there is no time limit, it depends on how quickly your team can achieve their objective), the matches can run short or run long. I mean a game can be over in 20 minutes but I've played games that are close to an hour.
And then, propose an alternative. Instead of the rule being "I can only play for 30/45 minutes", ask your parents if they will allow the rule to be "I can play one game of League of Legends."
Now on the weekend, you get 45 minutes, so you might say "Hey I can fit in 2 games if they go quick! We'll just stomp and force them to surrender at 20 minutes, two games in a row." but realistically, you can only fit one game into that time frame. If you try to start another game you'll just feel rushed and you probably won't enjoy it as much, and if you do have to disconnect because you're over the time, you'll just lose the round and may draw unwanted reports.
So instead you say, "May I play one game per day? This means that some days I might run a little longer. Maybe 40 - 50 minutes which is long for a weekday. But other days, I might get the whole game over in 20 minutes, but I can't play another game that day even on the weekends." So there is some give and take. Some days you won't get to play as long, others you may play longer, but each day you get a guaranteed one full length game. Thinking this out and presenting it to them will also make you sound more reasonable and show that you're giving this a mature thought.
Also, keep up on any of your chores or homework you have to do. LoL is fun but real life is more important; I know it doesn't feel like it now, but trust me. Plus, its a lot easier to make a deal with your parents if you can bring home a good report card or start the conversation with, "I've already done my chores" or something like that.
Good luck!