If you want, you can try to send in a support ticket using the link someone posted above to try and get the punished lifted. Unfortunately for you, though, your punishment is highly unlikely to be lifted.
The reasons for leaving a game are pretty much irrelevant, as they all have the same end result. If reasons did matter, people would likely make up stories to try and get out of punishments. Not that that's what you're doing, I do believe you and I am sorry for your loss, but I hope that you understand the point that I'm trying to make.
That being said, though, Riot knows that this is only a game and that real life stuff can happen that takes you away from the game, which is why they designed Leaverbuster with some leniency so that you don't get punished for only 1 or 2 leaves. You only get punished when you show a pattern of leaving multiple games. The fact that you have a 20 minute wait time shows that you used up that built-in leniency and then some, as the 20 minute punishment isn't given out for first time offenders. So, you're likely at the point to where leaving a few games will cause you to get another punishment, as you are on very thin ice using up that leniency.
If you truly to promise to never leave another game again, that's great, but you're still very likely going to have to work off the current punishment you have.
