What actions does Lucius perform that help the plot of Julius Caesar unfold?
Lucius is Brutus' servant, probably a young boy (judging by the way Brutus refers to him) and, looking at the play for his appearances, oddly enough, Lucius doesn't perform any actions which actually drive the plot forward.
In the orchard scene with Brutus, he gives the audience the crucial information that the "Ides of March" are coming up, and hands Brutus the paper that Cassius and his cronies have thrown in at the window. Most of the rest of the time, Brutus is lamenting the fact that Lucius is asleep and not answering his call.
In his next appearance (Act 2, Scene 4) Lucius is sent to run to the capital by Portia to find out what is happening at the Capitol, and to check that Brutus is OK. We presume he does it - but it's never specified by the play.
Lucius, of course, travels with Brutus to Philippi. And his final appearance in the play is in the "tent scene" (Act 4, Scene 3) where he plays his guitar for Brutus in order to try and sooth his nerves - and, in a neat throwback to his first appearance, falls asleep. Brutus treats him very, very tenderly and gently: showing a much more human side of his character.
But Lucius does not perform any key actions that alter the course of the play as a whole!
Contrary to the opinion of the previous answer, Lucius acts as a fill in character to keep the plot moving. He discovers the letter that has been thrown through Brutus's window, and, though not directly stated in the play, he informs Brutus's wife, Portia, of what has happened, setting in motion the thoughts that led her to commit suicide. So, he is not of great importance, but he keeps the plot moving.