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. Souls permanently grant 0.75 armor and ability power. Champions and large minions always drop a harvest-able soul. Small minions only sometimes drop a soul. Epic minions drop two souls.
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 8 seconds.