The puppy has been kept indoors for the past few days, and the cage never reappeared out back, so I think that they are going to keep Lightning inside where he belongs. The mother and son brought Lightning around to my house yesterday afternoon when they give me a piece of mail that had been misdelivered. Lightning seemed happy and healthy. I petted him and rubbed his fur, and he wanted to stay. The mother ended up carrying Lightning back home, but she did it gently, and she wasn't angry, so I think things are getting better.
I told them that I had ID'd Lightning as a Staffordshire Bull Terrier. Proper socialization will be critical, but he seems well-adjusted and friendly at the present time. I want to be sure it stays that way.
My next goal is to discreetly inquire about whether Lightning has been taken to the vet for a physical checkup, vaccinations, and heartworm treatment. The family had a dog 20 years ago when the mother was just a little girl, so I know that the grandmother knows how to care for a dog. I plan to ask the question about vet care the next time I see them outdoors. If they haven't picked a vet yet, I'll recommend my vet as well as the University of Illinois Small Animal Clinic.
We have another neighbor across the street who owns two dogs. They are very responsible pet owners. I might mention my concerns to them and ask them to look out for Lightning's well-being as well. I am of the philosophy that it takes a village to raise a Staffy
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Edit: Bella is in love with Lightning, but I'm not going to allow direct contact between them until Lightning has been taken to the vet for vaccinations and physical exam.