You correctly note that outer darkness describes any area outside the New Jerusalem. However, outer darkness and the Lake of Fire are one and the same place as the Lake of Fire lies outside the walls and gates of the New Jerusalem. In Rev 22:15 we find that the wicked unsaved are located outside the New Jerusalem. In Rev 21:8 we know that the wicked are in the Lake of Fire. From these two verses we can conclude that the Lake of Fire lies outside the New Jerusalem. The phrase "outer darkness" references the Lake of Fire's physical proximity to the New Jerusalem as the City gives off its own light, illuminated by the glory of God--anyplace outside the City is therefore outer darkness.
Having established this, there is a thought provoking question to be asked. Note that there is something peculiar about the gates of the New Jerusalem--the gates are never closed and always open (Rev 21:25). If the Lake of Fire lies outside the New Jerusalem, why would the gates always remain open? The question that immediately comes to mind is why would any of its inhabitants even want to venture outside of the City and leave God's presence only to enter outer darkness? Rev 3:12 confirms that no one goes out of it anymore. If no one goes out of the gates, why are the gates always open?