Is it against the rules to use a 3rd party website for item sets?

No. Item sets could have been made up by anyone. Whether it was you, another player, or a computer, it doesn't matter. Everyone allready looks to other websites for builds, so getting it from a calculator shouldn't matter, especially since math doesn't take many game play scenarios into account.

yes.

it is not only against the rules, but heavily illegal.

when they find out, you'll probably get imprisoned for the rest of your life.

Since you got two different inputs here let me confirm, Riot members have stated that this is perfectly fine, there are even programs that will adjust your in game item sets for you. Those are slightly riskier as if they are one that Riot cannot detect exactly how it is influencing your game then it is suspect of scripting and the like. In general though those programs are perfectly fine.

Looking up builds is completely fine and carries no risk though (other than looking up a bad/outdated build of course)