How do the decisions made by Juliet (including the decisions to lie to her parents about her marriage to Romeo) influence what happens in the rest of the play?

Without Juliet's decisions, the play never could have unfolded the way that it does.  She decides to keep her relationship with Romeo a secret; had she not, perhaps her parents would have prevented her from seeing him, perhaps they would have dealt with the fact that she married him -- we cannot know what their response would have been.  It is Juliet who prompts Romeo to marriage, a subject that doesn't seem to have crossed his mind until she raises it.  It is their marriage that makes Juliet so desperate not to marry the Count Paris and prompts her decision to remain true to Romeo after he killed Tybalt and to fake her own death.  Then, her decision to fake her death results in the miscommunication with Romeo; he never receives the message that she is not actually dead, and he takes his own life so as not to have to live without her.  Juliet's decisions to keep her relationship secret, to marry Romeo, and to fake her death to avoid marrying Paris propel the plot forward, forcing the next series of events to happen, and eventually lead to their suicides.