Offline mode and custom games?
League needs an offline mode. If your internet isnt connected or turned on, you should be given the opportunity to play custom games against bots, free from the interaction of other humans. In order for that to work, League would have to have some information stored on a profile on the hard drive to be able to know what champions, level, runes, etc. that the summoner has. It would only update while connected to the internet, so that IP glitching or other exploits would not be an issue, all it would need to be is a way to just burn some time or try out new tactics when internet is not available.
Also, custom games themselves ought to become truly customizable; currently, the only customizable thing about custom games is who you play with and on what map. It would be beneficial to allow certain game options such as starting level and gold ( and urf mode option!) in that players could actually try out new ideas for a full build, whose experimenting would not be reliant on getting the role and champion you want in a public match or having the opportunity to hit level 18 and obtaining enough gold for the desired items.
I only mention urf mode because due to the decreased cooldown and mana costs of abilities, players could practice complicated maneuvers that otherwise would be difficult or time-inefficient to rehearse, such as flash combos or other summoner spell usage, champion ultimates, or "sighting in" champion abilities (that it, with regard to skillshots, performing the ability over and over again to get a feel for it and improve accuracy drastically).
I believe that implementing these concepts into League could really help players and pros alike to strategize and plan for games, train mechanics, and just have fun in ways they otherwise just can't do often.