Today I started a new arena run after my old one got refunded from the changing of the card pool. I picked the priest card EVIL Conscripter twice in the run, but in my first game when I played them both the deathrattles did not trigger, I received no Lackeys after they died. They were not silenced at any point, but if it is relevant I had cast Mass Dispel before they both died (though I don’t remember if the second was in the field at the time).
Thinking back to the game, I remember my opponent playing EVIL Cable Rat as well but not playing any lackeys either.