Should Lowe's replace our area rugs that were soaked when the dishwasher they installed flooded the kitchen and hall?

If they have become damaged because of the water and their installation was faulty (they are the cause of the flood) then it would be reasonable to expect them to replace the the rugs. If they will not do so check on your house insurance cover and if this covers flood damage claim on that and explain what has happened. It will then become an argument between your insurance company and 'Lowe's.