Fiddlesticks was summoned from a plane nobody knows about, killed his summoner and is kept between the matches within the room where he was summoned first because, y'know, he slaughters everybody who enters.
As for Nightmare, he was living in the Summoners dreams (or I should say, their nightmares), à la Freddy Krueger, driving them mad from lack of sleep and some "never woke up", which I guess imply they were killed by him in their sleep. He went out of the "dreamscape" when a Summoner lost consciousness near a Nexus in the Treeline.
The rumors and campfire stories about Thresh speaks of a sadistic jailer who broke the body and mind of his prisonners with his chains, until he was hanged with his own chains during a riot/prisoner escape. He then came back as the wraith we know, as in every good ghost story. He now drag the soul of the deads back to the Shadow Isles.
So, not really related, as you can see; those infos are all in their respective official Lore, it takes only as few minute to verify. They're still all fairly interesting without it though.