That's a fascinating possible diversion. Lucrezia could have been dragging Klaus around in time to do things for her indefinitely. The apparent lack of Lucrezias in the current time who weren't instantiated in the current timeline suggests some limitations on time travel, but what? Other than Lucrezia herself (as seen in Albia's memories), has anyone been physically present in an earlier time? There are various examples of viewing earlier times, with two-way information transfer. Could Lucrezia have "traveled" back in time by copying herself onto someone from the distant past?

... that meandered more than I intended, but the core question about what time travel can actually do exists.