On June 20, 1920, Isaacson married Lula Maughan Jones in the Salt Lake Temple.

In the LDS Church, Isaacson was ordained a high priest in 1941 by Charles A. Callis of the Quorum of the Twelve Apostles.

However, President McKay had a great deal of confidence in Isaacson's judgement and past service.

Alvin R. Dyer was added as a counselor to the First Presidency to fill the role Isaacson was to perform.

Isaacson was released from the First Presidency upon McKay's death on January 18, 1970, and resumed his former position as an Assistant to the Twelve.