League of Legends Personal Lore Rankings (Not sorted within tiers)

Very High:
Ahri
Azir
Braum (PUNCH A MOUNTAIN.)
Diana
Leona
Lissandra
Nami
Orianna
Riven
Sion
Swain
Thresh
Vel'koz
Viktor
Volibear
Xerath
Yasuo
Zac

High:
Aatrox
Anivia
Ashe
Blitzcrank
Darius
Draven
Elise
Irelia
Jarvan IV
Jax
Karthus
Kassadin
Kha'zix
LeBlanc
Lucian
Malzahar
Nasus
Nautilus
Olaf
Quinn
Rumble
Sejuani
Soraka
Teemo
Twitch
Udyr
Vi
Wukong (Taking into account Master Yi's account of the encounter, lower otherwise.)
Zyra

Medium:
Bard
Annie
Caitlyn
Cho'gath
Dr. Mundo
Gangplank
Garen
Gnar
Graves
Hecarim
Jayce
Jinx
Kalista
Katarina
Kennen
Kog'maw
Lee Sin
Lulu
Lux
Master Yi
Mordekaiser
Morgana
Nunu
Pantheon
Rek'sai
Renekton
Rengar
Shyvana
Sivir
Skarner (Assuming his old lore about his race is intact and just moved to Shurima. If not, it drops to Very Low without a replacement.)
Sona
Syndra
Talon
Tristana
Trundle
Tryndamere
Twisted Fate (Could be bumped to a high if his lore was later fixed to better fit with Graves)
Urgot
Varus
Vayne
Yorick
Zed
Zilean

Low:
Akali
Brand
Cassiopeia
Corki
Ezreal
Fiddlesticks
Fizz
Gragas
Heimerdinger
Janna
Karma
Kayle
Maokai
Miss Fortune
Nidalee
Ryze
Shen
Veigar
Warwick
Xin Zhao
Ziggs

Very Low:
Alistar
Amumu (I didn't know he may have been changed to be a non-Yordle, though, that's new info)
Evelynn
Galio
Malphite
Nocturne
Poppy
Rammus (Moreso for being almost completely lore-less than having explicitly bad lore.)
Shaco
Singed (NOTE: The only lore Singed has is his old, explicitly non-canon Warwick apprentice lore, so I only had that to rate. If it was replaced with generic lore and his other contributions were kept, he'd be a Medium.)
Taric
Vladimir