Third Earth will eventually become the Land of Ooo.Just examine the two worlds back to back and it should be obvious. What other world could candy trees and robot bears exist in alongside undead wizards and robot death machines?
The Sword of Omens uses Mind Control.Once activated every Thundercat's eyes glow, they drop what they are doing that second and run off to help Lion-O.
Tigra's bola whip is a focus for his mental powers.In the first episode, he goes invisible without using the whip. Also, at least one episode displayed pyrotechnic effects when the whip struck. Not to mention the fact that Wilykat couldn't turn invisible with the whip when he and Wilykit "borrowed" the weapons.