We once had a couple of schnauzers who were die-hard barkers. Bark collars -- nope. De-barking -- nope. These dogs were gonna BARK. Part of it was our total ignorance of dog training.
Our current dog enjoys a good bark, but she's a pipsqueak. It's obnoxious, but not non-stop. Just when someone is at the front door (good girl) or when a large truck -- like a dump truck -- goes down the street (bad girl). She doesn't even find it necessary to join in when the neighborhood dogs are all out singing the song of their people. So she's not so bad.
Lucy is probably not so bad either, if they tried to find a reason for the non-stop barking. That's not normal for a basset.
Most renters are under a lease. Violating a lease usually means a stiff financial penalty, sometimes even having to pay the remainder of the rent for the rest of the lease and losing your deposit. So, it's not as simple as "just move."