To achieve the bottom route, you need to use a special save file that should have some mark not present on most of them. However, due to a known bug, the key doesn't appear on the bottom-most path when you're on that file, but if you access the beginning of the game, you should have a choice come up.
Whether the icon is appearing or not, if you go to the very beginning of the game before the route split down to that lock, the choice should appear, as long as you are on the file that is marked with a "TBC". If you don't have a file with "TBC", you simply have to autofill onto a specific segment (at the exact rightmost one you've played through already) and it should work.