Given that Archer had his own copy of the big red pendant, it stands to reason that Cu incarnated with his own pair of earrings.
The first time we see Bazett looking at her own reflection in the mirror, she doesn't have the earrings on. I think that was a way of holding off on the Lancer revelation. If we had seen them from square one, a lot of people would have been able to guess the connection right away.