Thresh does not gain armor per level. Instead, Thresh collects the souls of dead enemies by approaching them or by placing Dark Passage's lantern nearby. Each soul permanently grants 0.75 armor and ability power. Champions and large minions always drop a harvest-able soul. Small minions only sometimes drop a soul.
A soul will only drop if the enemy unit dies within 1900 range of Thresh. Souls are visible to allies, and only become visible to enemies if the enemy team has vision of Thresh. Souls disappear if not picked up after 14 seconds. 
Cooldown: 20 / 18 / 16 / 14 / 12
Cost: 80 mana
Active: After a 0.5 second wind-up, Thresh throws out his scythe in a line and forms a tether with the first enemy hit, dealing magic damage and stunning it for 1.5 seconds. Upon hitting an enemy, Death Sentence's current cooldown is also reduced by 3 seconds.
While the tether persists, Thresh cannot attack and he will periodically tug on the tether, each time pulling the target a short distance toward himself. After 0.5 seconds, or instantly if he hooks a minion or monster, Thresh can reactivate the ability to use Death Leap.
Active - Death Leap: Thresh pulls himself to the bound enemy. This removes the stun but allows Thresh to attack again. Thresh loses the ability to activate Death Leap when the tether breaks.
Cooldown: 22 / 20.5 / 19 / 17.5 / 16
Cost: 50 / 55 / 60 / 65 / 70 mana
Active: Thresh throws his lantern to the target location, which remains there for up to 6 seconds. If an ally right-clicks it, they pick up the lantern and Thresh pulls them both back to his own location. If Thresh moves more than ~1500 units away, the lantern will return to him.
For the next 6 seconds, allies who come near the lantern (even while Thresh is holding it) gain a shield that absorbs damage for up to 4 seconds. Allies can only receive the shield once per cast.
Passive: Thresh's basic attacks deal bonus magic damage. This value is equal to the total number of souls collected, plus a percentage of his attack damage based on the amount of time since his last attack.
Bonus Magic Damage: Souls + up to 80 / 110 / 140 / 170 / 200% AD
Active: Thresh sweeps his chain in a broad line towards a target direction. Enemies hit take magic damage, are knocked in the same direction as the chains, and are slowed afterwards for 1.5 seconds.
Active: Thresh summons 5 spectral walls around him that last up to 5 seconds. Enemy champions that touch a wall take magic damage and are slowed by 99% for 2 seconds, but break the wall. Once one wall is broken, the remaining walls deal half damage and apply half the slow duration. An enemy can be affected by multiple walls.