I don't believe the deaths of Romeo and Juliet was only due to the actions of Friar Lawrence but also due to fate and other characters e.g. Balthazar and Romeo and Juliet themselves.
As a priest, Romeo and Juliet trusted Friar Lawrence with their lives and went to him when they needed advice and solutions. He was there for Romeo and Juliet throughout their lives, he was the one who married them, came up with a plan to keep them together, and was a friend to them throughout all their tragedies. Shakespeare shows Friar Lawrence in a very positive light and he is liked by the audience which is another reason that the audience are reluctant to blame Friar Lawrence. Romeo is never shown with his parents in the play and at times Juliet's father is known to be a tyrant but in contrast Friar Lawrence is kind and caring towards both Romeo and Juliet and is also shown as a father figure to Romeo- 'Good morrow, Father'. The first time the audience see Friar Lawrence in the play he has a basket of herbs and wild flowers in his hand and seems a very sympathetic character and the audience immediately begin to like him which is why they may be reluctant to blame him for the death of Romeo and Juliet but in the end the audience see he is quite an ambiguous figure.
One of the reasons that the audience are reluctant to blame Friar Lawrence is because Tybalt is also very much to blame for the fate of Romeo and Juliet because he is determined to spill Montagues blood and Romeo's in particular which is ironic because in the end Romeo is the one who kills Tybalt, his cousin-in-law, and Romeo never had anything to do with the feud. Capulet is another character to blame for the death of the two lovers as it was he who insists on Juliet marrying Paris. If Capulet hadn't of done this then Friar Lawrence would never have had