Answer: Many players think that the administration keeps track if there are any changes in their IP addresses. And should they switch their main IP address for another, they will get a lifetime ban on the spot.
Of course, nobody cares about your IP address, as well as your in-game activity as long as you do not play in LCS or Challenger league.
In League of Legends, there are millions of players and tens of millions of accounts. It is likely that every player has entered the game with their account from an untypical IP address at least once in their experience. They might play from an Internet cafe, their friend’s home, being somewhere on vacation, or from their workplace (although one should not play the game while at work as there will soon be no money for RP). Have you ever gotten banned for things like that?