What is the relationship among Antony, Octavius, and Lepidus in Julius Caesar?

Antony, Octavius, and Lepidus form a political alliance and take of the rule of Rome as a triumvirate after Caesar's death. 

It can be argued that, of the three triumvirs, Octavius is the most wise and level-headed.  When Antony speaks of their fellow-triumvir Lepidus slightingly, Octavius challenges him, asking him how he can allow Lepidus to have the power to condemn people to death if he feels this way.  Octavius himself is "fair-minded and judicious", and his "commanding presence" appears to predict a positive and stable future for Rome.

Antony is a professional soldier and politician who has in the past had a reputation for being somewhat of a playboy.  He is athletic and possesses exceptional rhetorical skills; it is Antony who speaks so movingly at Caesar's funeral, inciting the crowd to riot against the conspirators.  As a triumvir, Antony works with the others to compile a list of men to be condemned, and he strikes a deal with Lepidus to allow the death of his own nephew in exchange for the life of Lepidus's brother, all the while scorning Lepidus as nothing more than a temporary "tool" in the newly formed government.  By the end of the play, however, it might be argued that Antony redeems himself somewhat, showing compassion by directing that Lucilius, who worked with the conspirators, be treated well, and by perceiving and declaring that Brutus, though a leader of the conspiracy, had acted in the common good.

Lepidus is the third member of the triumvirate, towards whom Antony is scornful while Octavius is supportive.  Little information is actually revealed about Lepidus beyond these conflicting assessments of his character.