Why did Lucy of future not know of the solution she wrote?
There's 3 (two for now) different future, first future is when the 10000 dragons come out from the gate. This future Lucy didn't know about Rogue so she didn't know that they have to destroy the gate so Rogue won't come to the past and prevent all of this to happen. So the diary didn't consist of how to stop the prophecy, but rather she just write what she know that if the gate destroyed, it will make a chain reaction effect. Present Lucy is the one who come up with the conclusion.