I am not sure about third generation, they would have to ask the people and see, plus do all the necessary health checks too. As to thinking about rescue labs, it really depends on who the person sells the pups to, when they sell pups they have to make sure (as any responsible dog owner should) that they go to 5 star homes. Dogs are put into rescue for many reasons, but why should that person not breed them just becuase of the amount of them in rescue? It is up to the breeder alone to decide that, sometimes the female dogs which we buy in as puppies are exceptional and you want to keep that line going, it is entirely up to that person.