Amumu. The poor little guy's cursed to a lonely existence due to his Touch of Death, yet he continues to wander Runeterra in search for kinship. No wonder he's called the "Sad Mummy".
Yorick's entire family is long dead, all traces of his life are long gone, and he's been trying to finally pass on for hundreds of years to no avail. His backstory just makes you feel incredibly sorry for the poor guy.
His rework somehow cranks this Up to Eleven; the last surviving monk of a religious order that was all but wiped out when a certain fateful accident struck the Blessed Isles, Yorick now spends his existence fighting the monsters of the Shadow Isles in the hopes of cleansing his home of this evil, with only his summoned undead and various spirits for company.
Riven deserves a mention. After what she went through leading up to her exile from Noxus, it's hard not to see why she left and went on the path to atonement.
Yasuo, for similar reasons as Riven's. Even after the true cause of his Elder's death comes to light and reveals that 1. Yas had nothing to do with it, and 2. it was no assassination, just an accident, he walks away broken, convinced he's the real guilty party because he wasn't there to prevent the accident.
Nautilus. Being left for dead sucks. Being left for dead while being dragged down by some kind of sea monster sucks more. Waking up on the friggin' ocean floor to find that you've been totally abandoned and that your suit has fused to your skin sucks even more than that. Making your way to land and finding that not only is your mind going, but that there are absolute zero traces of your existence really, really sucks. Poor dude.
In spite of her wackiness, Lulu could count. While she certainly enjoyed being in the Glade, she still fondly remembered Bandle City and even returned there, only to find out that centuries has passed and everyone who she knew and loved was long dead. Her attempts to reconnect with life in Valoran proved disastrous, and resulted in her being banished from Bandle City, now left to "seek out a vibrant magical place where those with unusual gifts were not just accepted but adored."