cover, lid, flap
葢 centers on something that covers or closes an opening: a lid, a flap, or the act of covering. The meanings all relate to placing a barrier over or on top of something.
葢 is a variant form of 蓋. It combines 艹 (grass) with 盇, which likely represents a cover over a vessel. The exact historical development of the 盇 component is uncertain.
The grass top 艹 sits over 盇, which looks like a dish with a lid. Picture a woven grass cover placed over a container to keep things inside.
For ガイ, imagine a guy named Gai carefully placing a lid on a pot: Gai -> ガイ, and the lid covers the pot.