What are three ways the church played an important role in the deaths of the lovers in Shakespeare's Romeo and Juliet?

The church--and more specifically Friar Laurence--played a tremendous role in the deaths of Romeo and Juliet by acting as an intermediary, negotiator, and "sanctuary" for their secret relationship.

The first person that Romeo turns to in order to confess the details of his sudden love for Juliet is Friar Laurence, a Franciscan friar who has grown tired of the conflict between the Montagues and the Capulets and is thus eager to help Romeo out. In Act Two, Scene Three, Romeo meets with Friar Laurence at his cell and begs him to agree to marry him and Juliet that very day. Although Friar Laurence initially expresses surprise that Romeo has so quickly moved past his feelings for Rosaline and "for doting, not for loving," he agrees to complete the ceremony for the two in hopes that it might turn their "households' rancour to pure love." He marries the couple in Act Two, Scene Six, with proclamation that "you shall not stay alone / Till holy church incorporate two in one." 

After Romeo kills Tybalt and is banished from Verona by the Prince, he rushes back to Friar Laurence for help. Friar Laurence calms the hysterical, suicidal boy down and encourages Romeo to leave town until they can work out a plan for his clemency. With Romeo gone and Juliet newly engaged to Paris at the orders of her ruthless father, Friar Laurence remains the only adult man who is fully aware of all the details of the situation and capable of helping the couple. He devises a plan to reunite Romeo and Juliet: Juliet will take a sleeping potion that makes her appear dead, and Romeo will meet her in the family crypt once the Capulets have laid her to rest. Friar Laurence sends out a messenger to inform Romeo of the plan, but he fails to reach Romeo in time. Believing that Juliet is actually dead, Romeo buys poison from an apothecary, drinks it in the tomb, and falls dead alongside his beloved. Juliet awakens to discover her newly dead husband and throws herself upon his dagger, dying as well. If it had not been for the poor planning of Friar Laurence--or at the very least the poor execution of a semi-decent plan--Romeo and Juliet may not have died in such a devastating manner. 

So, in short: the church enables Romeo and Juliet to carry out their hurried passions and to deceive their families--an act that winds up being fatal for this young, foolish couple.