Lifetime means as long as American Express sees you as having had a card in the past. Often that seems to be around seven years. You can ask American Express what cards you’ve had in the past and they’ll tell.
There’s no more guessing, because American Express has a new popup when you submit an application — before they pull your credit — noting you’ve had the card in the past (or currently have it) and therefore aren’t eligible for a bonus. You can proceed with the application if you wish, or stop the process.