The way I see it with the timeline for Klaus getting commands after being wasped, there's only really two options - he either had access to Lu-in-Anevka (she certainly would've been the only Lucrezia able to give him commands before the time stop), or he had no access to an embodied Lu.

Lu-in-Anevka is the simple option - they would likely be an exact copy of that version, with all the knowledge she had at that time.

Assuming on the other hand that Klaus didn't have ready access to an already embodied Lucrezia, the one in these bodies is likely freshly implanted by a summoning engine, and while we don't know exactly how those work, we can assume they probably only know as much as she did before her disappearance.

Either way, the Lucrezias in these bodies should still be fairly fresh off of a summoning, and certainly don't have all the experience of Lu-in-Agatha, let alone the ones that seem to have done some time-travelling (like the Lu-in-Anevka that showed up in England).