Eclipse IS going to change the world, just now the way they expected it ...
There's nothing suggesting that Dark Rogue is from another timeline as Future Lucy. It's still plausible that they are both from the same time/era.
How does he know that she's going to close the gate? She didn't HAVE to have been the one to close the gate back then, but if he knew that she was jumping back in time
with that intention, then of course he can lie and say that she 'closed' the gate.
Also, how does he know that she
can close the gate? It's more than likely that she's the one that opened it on their end in the first place and it stands to reason that if one can open it, one can also close it.