Accounts that go unused for too long are susceptible to Summoner name decay. If an account hasn't played any games for a certain amount of time, their Summoner name will be flagged as available. The Summoner name remains on the account until another player claims it, at which point the Summoner name will be removed. If an inactive account loses its Summoner name this way, there will be a prompt to select a new Summoner name the next time that account logs into the client.
3 Years is set out as a general rule because there is always a chance people may come back and reclaim the account. However, accounts such as the one you have mentioned, claiming the name and then never playing again, were generally made right around the start of the game (2007-2009) however, and so are well open to being claimed by now.
It may be worth contacting an admin if there is a specific name, however the likely answer will be to wait for the three years, or a compromise of sorts, as the process is the same for all.