I'm sure most reasonable people were busy taking Desmond's condition seriously. Psssh.

BUT... I am just going to assume that the conversation about Lucy happened at some point while they were in the temple. It would make very little sense for the other Assassins to have seen Clay's memories, given that Rebecca continues to refer to him as 'Subject 16' - which is still a bit odd, since she supposedly worked alongside him.

... And I think I am attempting to inject too much logic into this.