Hemingway just about sums it up when the old man asks: "Why are the lions the main thing that is left?" What a fantastic question. The old man, we are told, "no longer" dreams about people – just the places, and namely the lions. You can go a few directions with this. First, the lions are a memory from his youth. Much of his struggle with the fish is about proving that he’s still there. The old man has a statement to make: he’s still around, and he’s still rocking the boat. In other words, his past, including the lions, isn’t just a distant memory.
The other question is, why lions? Why not geese or alligators? To start off, lions are strong creatures, predators, hunters, just as the old man hunts the marlin. They’re also the head honchos. Even though they’re at the top, they have to go out every day, hunt, and prove that they’re, well, still the head honchos.
Where are we getting this from? Take a look at paragraphs 76 and 77 on day three (right before the memory of arm wrestling). The old man says he needs to prove that he is a strange man. "Strange" doesn’t mean weird here, rather unique, different. It is the old man’s strangeness that enables him to be alone on the sea doing battle with a marlin for three days, just as he calls the marlin "strange" for not being tired. But back to the proving part. The old man has to prove, in a sense, his strength, his prowess, his abilities. And he talks about having to prove it rather elegantly for a paragraph. The very next paragraph is about the lions. See the connection?