John A. Tvedtnes records in personal journal Harold B. Lee saying 2nd Anointing is not necessary for exaltation.
John A. Tvedtnes, Journal, June 30, 1961, in David John Buerger, "'The Fulness of the Priesthood': The Second Anointing in Latter-day Saint Theology and Practice," Dialogue: A Journal of Mormon Thought 16, no. 1 (Spring 1983): 43n123
When John A. Tvedtnes, for instance, asked Apostle Harold B. Lee in a Salt Lake Temple missionary question-and-answer session, if the "second endowment" existed and, "if so, what connection does it have with the Holy Spirit of Promise, and who receives it and why and how?", Lee answered, "You don't have to worry. You've received all the ordinances necessary for exaltation. .. . It is a special blessing given by the President of the Church to men who have been called. It is not necessary to receive it, however. You have all the endowment you need to be exalted." John A. Tvedtnes, Journal, 30 June 1961; recounted by permission.