How to make it not clone but move it to workspace? (ANSWERED)

First of all, it is incredibly bad practice to double the event structure like that. Instead, use an elseif structure within the one you already have:

admin = {"Player",} 

game.Players.PlayerAdded:connect(function(nP)
	for _,v in pairs(admin) do
		if nP.Name == v then
			nP.Chatted:connect(function(msg)

				if msg == "lockgate" then 
					--Since you never did anything with the Message you created, I removed it from your code.
					if game.Lighting:FindFirstChild("GF") then --If the gate isn't there, we will run into an error on the next line.
						game.Lighting.GF.Parent = game.Workspace
					end

				elseif msg == "unlockgate" then 
					if game.Workspace:FindFirstChild("GF") then --Same as above.
						game.Workspace.GF.Parent = game.Lighting
						--It's a much better idea to have this in ReplicatedStorage, but it is not strictly necessary.
					end

				end
			end)
		end
	end
end)

I believe the problem you were running into was that you were trying to move the parent of a non-existent object. That is, your script errors when trying to move the object if you've called the commands in the wrong order.