I need help writing a paper on the character Lucio in Shakespeare's play Measure for Measure.

I moved your question to the Measure for
Measure Group, because it seems that information about the character Lucio is
really what you are seeking.  Here are some questions to consider about Lucio that will
help you create a thesis statement, the first step in writing any
paper.

The following questions are meant to help you
consider how you see Lucio in the play.  Each of them can easily be changed into a
statement, creating a thesis upon which to build an essay that provides examples from
the text to support your thesis.  Here are the questions to consider about
Lucio:

• Is Lucio a true friend to Claudio?  Why
  or why not?


• What are Lucio's motives in the play?  Does
  he act for the good of other characters or does he simply desire to stir up
  trouble?


• Is Lucio a character who speaks truthfully? 
  Does he every contradict himself?  What might the consistency (or lack of consistency)
  in his speech tell the audience about his character?


• Does
  Lucio operate as a foil to the Duke?  If so, which characteristics of the Duke does
  Lucio highlight by providing an opposing
  example?

This list of questions is certainly
not meant to be exhaustive, and you may have a very different idea for a thesis
already.  Here is an abbreviated list of steps (link below) from the Entoes page, "How
to write a Character Analysis," which might also
help:

• Pay attention
  to the character’s ethics.


• Decide whether the character’s
  actions are wise or unwise.


• What is the character’s
  motivation?


• Consider the effects of the character’s
  behavior on other characters.


• Is the character “flat” or
  “round”?

Please
follow the links below to more on Lucio and writing a character
analysis.