The Truth
The truth of what was going on was pretty simple. Bronx had been watching Julia sleep, as he had a traumatic upbringing. He was most likely abandoned while he was sleeping and felt the need to remain awake when he felt most vulnerable, which was at night.
And he brought the puppy home because he felt neglected when Julia locked him in the kitchen. But he soon realized that the ill puppy could harm her. And he wanted to prevent that.