No one mentioned that Yamato bridge from "Lease" is different than the one seen in "Contagion".
But the Yamato bridge from "Lease" wasn't real. And there were two of them.
Exactly my point. The whole thing is a bad fascimile by the alien. The ship wasn't made of tritanium as Riker remarked, and Worf made it sound like the bridge is different from Enterprise's and he knows the layout. When they get there, it's same exact bridge, so either Worf was lying, or the alien coudn't recreate the real one. Having rewatched this episode, I am now of the opinion that the registry was faked too:
The alien saw the registry on the Enterprise, but was not able to read their computers, so it tried to replicate something similar, an NCC prefix, followed by four numbers, followed by a dash and letter. Riker simply read it from the screen, and never bothered to double-check Starfleet ship registry in the computer.
The only mystery in this case would be how it managed to come up with the name Yamato? Perhaps it pretended to be a crew member and gleaned it from a screen somewhere or simply asked somebody.
PS. You might ask why he can't read the computers, well it's just an assumption based on the fact that the whole experiment would be useless if he could get into LCARS and find out about the meaning of death, or find out about males and females, or make the computers on the fake Yamato work (corect me if I'm wrong on this one) etc... I think the whole episode is based on him being far from omnipotent.