Friar Lawrence could have prevented Romeo and Juliet’s death by not giving Juliet the potion.
Many characters in the play might have made different choices. Romeo might not have gone to the ball, Juliet might have agreed to marry Paris, Tybalt might not have fought Mercutio (and the other way around), and the parents might have chosen to end the feud. Yet the one person whose choice was most influential was Friar Lawrence.
Friar Lawrence clearly cared about Romeo, and wanted to help him. This is why he agreed to give Juliet the potion. The problem is that in doing so he set in motion a series of events that caused both their deaths.
If Friar Lawrence had not given Juliet the potion that mimicked death, Romeo would not have gone to the Capulet tomb and killed himself because he thought Juliet was dead. This is what caused Juliet to kill herself as well.
Friar Lawrence is fully aware of his guilt. He confesses to the prince that he was trying to do something good.
All this I know, and to the marriage
Her nurse is privy; and if aught in this
Miscarried by my fault, let my old life
Be sacrific'd, some hour before his time,
Unto the rigour of severest law. (Act 5, Scene 3 p. 114)
He is forgiven, it seems, but Friar Lawrence will still have to live for the rest of his life knowing that he did end the feud, but at what cost?
There is no one person responsible for the tragedy in this play. Each character makes a series of choices that end in fated doom.