I've never seen a Landlord in my game who also roams around in the city doing really weird things, but who knows that it may happen. In any case a Landlord is always generated separately from the CL Weirdos as far as the game is concerned. Plus if you do play the Landlord, just know that they will no longer be your landlord and if they had the weirdo trait they would no longer be one once you play them. I know from experience since I discovered 2 immortal weirdos who I now play have begun aging since I started playing them.