Why does Juliet seek help from Friar Laurence?

To answer this question, take a look at act 3, scene 5. In this scene, Juliet argues with both of her parents about her impending marriage to Paris. Of course, the reader knows that Juliet cannot marry Paris because she is already married to Romeo, but Juliet's parents have no idea that this has happened, and so they will not listen to her protests about not marrying Paris. In fact, the marriage to Paris has already been arranged for Thursday, which is just a few days away.
Juliet, therefore, decides that she will seek out Friar Lawrence to find a solution to this problem. Perhaps she believes that as the Friar is due to perform the marriage to Paris, he might be able to run some interference and create a delay. This is certainly suggested in the next scene (act 4, scene 1) in which we see Friar Lawrence encouraging Paris to postpone the marriage to Juliet.
But, for Juliet, if Friar Lawrence cannot provide the help she needs, she is determined to take her own life. This is a clear sign that she will not give up on Romeo or on determining the course of her own life.