Leage Of Leagend how long will it live?

If you mean dead as in shutting the servers down and no longer being able to log in, probably 25-30 years. I know this sounds weird, but let's look at online games from the last 20 years.

Ultima Online came out in 1997 and there are still a lot of people paying a subscription fee each month to play that on the official servers, despite the fact there are actually more people playing on free/private servers. Why the fuck would people still be playing that game? Well basically nothing has come out that does what it does better. That game will not die for at least another 20 years until something finally comes out to replace it, and there is a good chance that nothing will. Why is this? Well think about how much money online games make now through microtransactions and sponsorship. The big dogs of the industry buy up anything that makes a shit ton of money, so it's going to hard to get funding to make a game that isn't designed specifically to make money. A lot of games have tried new ideas and crowdfunding, but they rarely work because not enough people support the project. Eventually what happens is the games get released unfinished and buggy, or they simply sell it off to another company who does nothing with it and the game dies.

World of Warcraft is almost 20 years old and it still makes billions of dollars in subscription fees. We will see what Microsoft does with it in a few years when the transition happens, but they didn't pay 80 billion dollars without a plan to make that money back. Unless they really fuck that up, it will be around for at least another 10-15 years.

Eventually Riot will make a new game to replace League of Legends and shut down the old one. If for some strange reason Riot goes out of business they will just sell it off to someone else, who will probably run it for at least a few years unless it drastically flops. There is also a good chance if that does happen, someone will make a free/private server which will always have players on it.