I truly believe that League of Legends should incorporate a sort of Phone Authentication to prevent hacked accounts and overall account security. Counter Strike has a Phone Authentication service that actually prevents smurfing aswell. its called prime and you can only connect one cell phone number per account.
2 step authentication is long overdue in League. Mobile support for their websites is still fairly new, so maybe if we're lucky we'll see 2 step authentication in a few years time.
It's something being worked on (I heard it was available on the PBE), but they may need to wait for the new client to drop to implement it. I don't have any concrete news yet.
Personally, I'd prefer an authentication system similar to Steam.
Whenever you login from a new device, a verification email is sent to your associated email account with a code required to authorize the device.
You will only be prompted once per unique device rather than once per login attempt.
Not everyone has a phone you know...
