Since League of Legends just happens 1 game at a time, it doesn't really make sense... Every time when you're done with a game you come to the launcher screen, where the time on your computer is in plain view. Realizing what time it is when you're actually IN a game won't help at all, because you've already started the game, and if you leave you'll be reported for being AFK/quitting anyways.
If, however, the game was always full-screen, and didn't have a definitive start/stopping point this would make sense. But since it does, there's really no point to an in-game clock.