Daddy Had a Good Reason for Abandoning You: As Lucky's father Slick explained in "I Never Barked For My Father", Lucky had to stop thinking about it as a puppy and think about it from his father's perspective, or for you as the viewer, as Slick's role as a pet. Slick was actually the dog of the neighbors of Lucky's mother's humans, not of his mother's humans as Lucky thought. When the neighbors moved across town, they naturally took Slick with them.)
Oblivious to Love: In "Olaf In Love". Though both he and Cookie nervously denied their feelings when Kiki, the featured puppy, made mention of them being "more than friends", Cookie pointedly brought up of Lucky's blindness to her feelings (and his own?), in relation to Olaf dating city librarian Gertrude Washburn.
When You Coming Home, Dad?: When Lucky was a puppy, his father would be gone for hours or even days at a time, until one day he left for good. As noted above, this is because his dad belonged to another family.
Sassy Black Woman: Downplayed. While she lives with a multiracial family with a black father, none of them speak in the manner that she does.
Tertiary Sexual Characteristics: Cookie is a bit more complicated. At first, she didn't have anything. (Her collar is black.) After seeing Dolly flirt her way into getting the male dogs to fawn over her in the episode "The General", she becomes jealous. By the end, Dolly gives Cookie the pink bow that she's seen with from that point on.
A group of Pound Puppies in-training. While they formed in season 2, although Rebound has made regular appearances since the third episode, and Cupcake debuted in "Mutternal Instincts". When Patches was introduced, the club was formed and they have rarely been seen without each other.
Tropes Applied to The Super Secret Pup Club as a Whole