Brining rack of lamb
Why do you want to brine it? First, there really is no such thing as dry brining.  It is salting. When brining, however, only salt and water penetrates. The result is a moister end product, but, depending on how long you brine, it can also change the texture.  Some people enjoy brined proteins, others don't.  Brining can also be used as a crutch in potential over-cook situations (like turkey, which has parts that cook at different rates).  I would not brine lamb rack.  You are probably going to cook it rare, to medium rare anyway, so there is no chance of drying it out.