The only way for energy champions to increase their energy regen, or even maximum energy, is to buy the runes associated with energy and energy regen.
What you probably haven't noticed is that most energy champions already DO have their own "energy efficiency per level" mechanic, in the form of adding points into ability rank. For instance, Shen's E energy costs go down with every rank, as well as Akali's W+E.
Lee Sin is the only one that doesn't get reduced energy costs per ability ranking, but that's because his passive gives him insane energy refunding already.
Looking at your match history, it seems you're trying to be a Kennen main. Here's a link to his page so you can learn more about him:
http://leagueoflegends.wikia.com/wiki/Kennen