I've been running Labyrinth for quite some time now, but all I got was Midnight Wedding pieces.
Which Doppelganger has the Lorica Plated? The last one, right?
It doesn't matter which doppelganger you kill. The item drops are random. From personal experience, I've gotten all sorts of armor from each type of doppelganger, so just kill them as quick as you can without choosing