Lobotomized Strongman: Non can use Super Strength. In addition to the normal effects, when using an object during an attack, increase the damage dealt by 1.

If Non has successfully picked up a Relic like the Crimson Gem of Cyttorak, does that count as "using an object during an attack"?
No. The Relic on the character card is not used during the attack. It may have some type of effect on the attack (like, say, by modifying a combat value), but the Relic itself is never actually involved in the attack.