Can you check in-game by going to portal -> world -> timeline (top right) -> hover over the Season of the Witch icon next to Lightfall. It'll say whether its owned at the bottom (or nothing if it isn't), if it doesn't say owned then there's your answer. With the above said, given its beyond the one season limit Bungie set for them officially supporting, there's not really much here will come out of it and will likely want to directly contact the Wayback Machine either via Github or their Reddit account to see if they are able to provide any workarounds through the extension.