You said you already lowered your graphics settings, but make absolutely sure that Ambient Occlusion is turned off.

You probably already did this as well, but reset your router, and consider re-installing FFXIV (doesn't take that long). You may even go as far as deleting the FFXIV Folder under your My Games directory. This will delete saved UI and character model data, which isn't that important - along with other information that is stored locally. All in all, this is still a shot in the dark.

You wouldn't be the first to suffer from a completely untraceable form of lag in FFXIV, sadly.