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.
The best answer is unequal. Cassius and Brutus struggle with one another, and Brutus clearly dominates the decision making, but they are friends. Cassius calls Brutus his "brother" at one point. However, the triumvirate of Antony, Octavius, and Lepidus is presented as all business, and Octavius clearly leads the pack. Antony doesn't like Lepidus, and feels he is not good enough to have power. Antony, in other words, is a snob. Octavius argues that Lepidus is a “a tried and valiant soldier”; he says that Lepidus is good enough to do work for them, he is good enough to have power.
Besides this scene, Octavius overrides Antony on the battlefield, refusing to fight where Antony tries to order him to. This tension between the three proves three things: 1) that power is corrupting, as seen in Antony's behavior towards Lepidus; 2) that this triumvirate, though they may be successful, can not last (as we know from history; and 3) that Octavius is the must judicial and forthright leader, thus likely to be the new leader (again, as we know from history). Shakespeare includes many scenes to suggest the lasting effect of Caesar, even though he is killed so early in the play - such as the appearance of his ghost. The strength of Octavius in the triumvirate pushes this idea further, as Octavius is, after all, a Caesar by blood. Shakespeare is showing the idea that there was Caesar the man, killed by the conspirators, but also Caesar the idea, that of a single, strong leader, a monarch.
The relationship between Antony, Octavius and Lepidus is a formal and strictly professional one. They are not friends nor are they “brothers” this alliance is simply business. These three are together in the name of vengeance as was injustice was imposed upon their loved one (Caesar). Having a common motive and enemy makes this alliance work, however without the conflicts that bind this relationship we find that it is strained and raises the inevitable question of who is to be in power? Shakespeare is able to bring out this conflict between The three much before the actual battle at Philippi. Lepidus is like the third wheel. He bears no importance and lacks any true purpose. His ability to lead is constantly mocked by Mark Antony. In fact his very presence in the triumvirate is questioned. The two strong minds in this relationship are clearly Antony and Octavius. Mark Antony views Lepidus as nothing more than a boy who best run errands stating in Act 4.1
“ This is a slightest unmeritable man, meet to be sent on errands”. But Octavius on the another hand states in Lepidus’s defense “ But he is a tried and valiant solider.” To which Antony cleverly reply’s “ So is my horse” (a simile comparing the horse to Lepidus) It is evident how brilliantly Shakespeare is able to bring out not only each of their views on Lepidus but also give some hints to the reader about their personalities