Actually, the lion trainers choose to have ALL of the lions in their performance, but the "star of the show" is always the "one with the lowest social standing in the pride" otherwise know as the "omega animal."
In other words, the lion that is chosen to be the star is the one who is on the fringe of lion society, so to speak. The other lions (the "alpha" lions) in the pride are present, but are simply sitting on the sidelines on barrels.
Why is this so? Because this omega lion "has the most to gain from a close relationship with the super-alpha trainer." Pi mentions the security that the lion receives from his treatment: not only extra snacks but also protection from the other alpha lions. Pi is also sure to mention that this happens in zoos as well. Many omega animals are the ones that become the closest to their zookeepers.