Captain Lonestar has lived most of a life where he had to do everything by himself and thus isn't accustomed to working with others.
Captain Lonestar gains power from an inverse form of the Power of Friendship, thus he refuses to need companions.
Inverted: Captain Lonestar suggests that the team should disband and their members should each go off on their seperate paths, but they decline because they always work together.
Subverted: Captain Lonestar declines to join the team when offered, but later it turns out that he had been working with a different team all along.
Double Subverted: ...But this is actually a ruse to get the original team off his back by continually pestering him about the benefits of working together.
Parodied: Captain Lonestar has invented a special radar that will alert him to the presence of anyone in the vicinity who might be of help to him so he can avoid working with them at all times.
Zig Zagged: Captain Lonestar clearly prefers to work alone, and will often refuse help. But he will sometimes reluctantly accept it if the job looks particularly tough, and once in a great while will even ask for help in advance.
Lampshaded: "Looks like Captain Lonestar is going off on the mission on his own again."
Invoked: Having pledged to always work alone, Captain Lonestar recognizes that he can't break tradition just because the situation is grim.
Exploited: Because he doesn't work with anyone, the other heroes tend to view Captain Lonestar with suspicion and distrust; it's remarkably easy for the villain to frame him for some heinous crime, and sit back and watch while the other heroes take him out.
Defied: Captain Lonestar normally works alone, but recognizes that continuing to do this may cost him his life, and joins the team.
Discussed: "Why does the brooding loner in these types of situations always refuse help even though he’d beat the bad guy in five minutes flat if he did?"
Conversed: "Why is Captain Lonestar such a loner? Does he have a Dark Secret?"
Captain Lonestar ends up failing more often than not due his insistence on always working alone.
No one really trusts or likes Captain Lonestar; on the one occasion when he really, truly needs an ally, there's no one to help him.
Reconstructed: ...But all those missions were nigh-impossible to accomplish with a team. Those he did he only succeeded at specifically because he was working alone.
Played For Laughs: Captain Lonestar always works alone because in reality he's a bumbling idiot.