The priest speaking to Lara in the church is Richard Burton
At the 14m45s mark, a priest speaks at the burial of young Yuri's mother. His hair and beard are long and silvery white. I believe this priest is rightly listed on IMDb as "José Nieto (uncredited)," who would have been 63 years old the year Dr. Zhivago was released.
http://800spaghettiwesterns.blogspot.com/2012/01/jose-nieto.html
The following scene, which is less than 30 seconds long, occurs at the 44m09s mark.
Priest: "You know what Our Lord said to the woman taken in adultery?"
Lara: "Yes, Father, he said 'Go, and sin no more.'"
Priest: "And did she?"
Lara: "I don’t know, Father."
Priest: "Nobody does, child. Flesh is not weak; it is strong. Only the sacrament of marriage will contain it. Remember that."
Lara: [Nods, bows and walks away.]
The priest in this scene is clearly not the priest who spoke at the burial. I have no doubt that the actor playing this priest is Richard Burton. The voice absolutely clinches it.
This is a topic that has come and gone and now come again.
If the priest in the church is not Richard Burton, who is he?
Good excuse for watching the movie again.