People live in RVs. The real question is: is it practical to have an airship with the top covered in photovoltaic cells sufficient to run all your normal electrical needs?

A residential-class airship would probably be limited to visual flight rules conditions and have to land or at least be docked every night. You'll want to do that for a variety of comfort reasons, too -- water is heavy, so finding a campground with electrical and water hookups would be preferred.

Storms could be an issue - storm won't usually sink a houseboat or destroy a RV trailer.

But it might very well smash a residential airship into the ground even if securely moored just due to the sheer size of its gas envelope being effectively a giant sail.

> Would it be possible to live on such a ship?

People live on house boats smaller than early Zeppelins. The challenge will be supplies and human excretions - if you live on such a thing and it's anchored over land you can't just drop your feces on a whim.