It's a good idea to note that Lucio is the one who finds outs that Claudio is being arrested, and Lucio is the one who goes to Isabella, for Claudio, to ask for her help. Lucio's main appearance is basically for comic relief, but he also has a place in the plot line.
It's also a good idea to note that Lucio accompanies Isabella to appeal the release of her brother to Angelo. While Isabella pleads for Claudio's life out of sisterly love, she also can't help but to agree with Angelo that what Claudio did was wrong. Therefore, Isabelle finds it difficult to completely beg for her brother's life, and Lucio is the one to edge her on and tell her to try harder.
Act 2 Scene 2, lines 45-51
ISABELLA: "Oh, just but severe law!" (Exemplifies Isabella's difficult predicament)
LUCIO: Give't not o'er so. To him again, entreat him!
Kneel down before him; hang upon his gown.
You are too cold. If you should need a pin,
You could not with more tame a tongue desire it.
To him, I say!