When the Leviathan plays the Luna Cannon card and during an an encounter uses its ability to take the worldship and place it on the hyperspace gate, does the Lunar Cannon take part in the encounter?

No. For one thing, the Lunar Cannon is no longer "next to" the worldship while it is away. But even if it were, it wouldn't help because the Lunar Cannon only Defends Two Planets: it protects a planet only when it is the target of an encounter.