Thresh vs Nautilus Support Matchup

How to play as Thresh

Use your 450 attack range and charged Flay(E) passive to harass Nautilus when he steps up for a minion; stay near your wave so Dredge Line(Q) can hit a minion instead of you. (Unverified: no source confirms this note.)

If Nautilus is pulling himself toward you with Dredge Line(Q), time Flay(E) to knock him away before he can follow with Staggering Blow(P); casting too early may miss the dash.

If Nautilus targets an ally with Depth Charge(R), place Dark Passage(W) under them so they can reposition after the knock-up and avoid the enemy team's follow-up. (Unverified: no source confirms this note.)

With correct timing, Flay(E) can interrupt Nautilus's Dredge Line(Q) dash and create space before he reaches the target; a late Flay may still leave him close enough to land Staggering Blow(P).

Thresh possesses 450 basic attack range compared to Nautilus's 175 melee range, allowing Thresh to safely harass Nautilus with Flay(E) passive on-hit magic damage from behind minions.

How to play as Nautilus

If you have a ward available, try placing it on Thresh's Dark Passage(W) as his ally approaches; obstructing the click can delay their escape long enough for your team to respond. (Unverified: no source confirms this note.)

A ward or another targetable unit overlapping Dark Passage(W)'s lantern can make it harder for Thresh's ally to click and take the dash; this is a situational obstruction, not a guaranteed block. (Unverified: no source confirms this note.)

Sources

These notes come from LoL Wiki and mobafire.com, checked against the champions' abilities.