Given Threshes theme/lore/character, you wouldn't think that he is a support.

No, I am not saying he shouldn't be a support. As supports go, Thresh is pretty badass, and that should remain his main role. I am just saying that there are roles that could better suit his theme.

I remember when I first started playing this game, I looked at Threshes splash art/lore, and "support" was the last thing I thought.

Thresh is a demonic jailer, whose soul (ha, see what I did there) purpose is to hunt people down, kill them, and torture their souls for eternity.

Just look at his old lore.

Thresh is a twisted reaper whose hungry chains ensnare the souls of the living. A moment's hesitation at the sight of his ghostly visage and there is no escape. He leaves in his wake hollow corpses, their souls ripped loose and trapped in the sickly green light of his lantern. The Chain Warden takes sadistic joy in tormenting his victims, both before and after their deaths. His grim task is never complete, and he stalks the land for ever more resolute spirits to unravel.

Thresh carves careful, deliberate paths through Valoran. He handpicks his targets individually, devoting his full attention to each soul in turn. He isolates and toys with them, gradually eroding their sanity with his twisted, maddening humor. Once Thresh takes an interest in a soul, he does not relent until he possesses it. He then drags those he captures back to the Shadow Isles for an unimaginably dreadful fate. This is his only purpose.

Little is known about the Chain Warden's past, and many of the details live only in nursery rhymes and campfire tales. They tell of a sadistic jailer from centuries past who took great delight in torturing his wards. Patient and brutal, he used a variety of methods to break his victims' minds before their bodies succumbed to his grisly designs. Chains were the jailer's preferred instruments of terror. Their shrill scrape marked his dreadful approach and promised agony to those he visited. His dark reign went unchallenged until his prisoners escaped during a massive riot. They overwhelmed him, and without ceremony or remorse, hanged him from his own chains. Thus began the unlife of the horrible specter known as Thresh, or so the tales go.

Thresh now haunts the land, leaving an aftermath of horror and despair. However, there is a devious purpose behind his dark machinations, and the meager spirits of average men are insufficient. He seeks stronger souls. Only when he has broken the wills of Valoran's most resilient warriors will he finally have what he needs.

He stalks the land, hunting people down to torment for eternity.

That doesn't sound like a support, that sounds like a jungler.

So... what if he had that capability as well as supporting?

He wouldn't really need any massive changes. His kit is already great for ganking, and he can clear the jungle, if just barely.

Something as small as "Flay now slows the attack speed of jungle monsters" would make him capable.