Lozano was born to Mormon parents in Tula, Hidalgo. He was the eldest of 13 children. His mother had been an employee of Rafael Monroy, who was slain during the Mexican Revolution of 1910 in large part because of his belief in Mormonism. Lozano's father, also named Agricol, joined The Church of Jesus Christ of Latter-day Saints (LDS Church) after learning about Mormonism from his wife.
As a child, Lozano often helped his father in the brick-laying business. He went to Mexico City to become a professional soccer player but never made the team. Instead he became a missionary for the LDS Church. After his mission, Lozano was a custodian at the Museum of Anthropology and History of Mexico. It was largely because of a sermon he heard from Spencer W. Kimball when he was on a trip to the Mesa Arizona Temple in the 1940s that Lozano decided to pursue a life as a lawyer and an advocate from the indigenous people of Mexico.
Lozano served two full-time missions for the church in Mexico.
Lozano was for many years the Chief Counsel for the LDS Church in Mexico. He was one of the key figures in getting the church legal recognition in the country in 1993.
Lozano was the first Latino to serve as a stake president in Mexico. He became president of the Mexico City North Stake in 1967. Prior to this, he had served as a counselor in the first stake presidency in Mexico City. Lozano served as president of other stakes due to rapid church growth and divisions of stakes from time to time.
Lozano served as president of the Argentina Bahía Blanca Mission. He was also a Regional Representative of the Twelve Apostles; in this capacity, he would often emphasize that the Mexicans needed to step up and take part in leading the church in Mexico. Lozano was also involved with the Church School board in Mexico. Lozano also worked for a time as the general counsel of the LDS Church in Mexico.
Lozano is also the author of several books. His Historia del Mormonismo en México (1983) (ISBN 9687207000)  is aggressive in its assertion that the Mexican people have a special place as part of the house of Israel as descendants of Lehi in the Book of Mormon. Other writings of Lozano include his short Jesús el Cristo en la Biblia (1983) and his much longer La Apostasia (1982). A 1980 work by Lozano was Historia de la Iglesia en México which has the same general subject as his 1983 work.
- Deseret News, 3 March 1995.
- Church News, October 23, 1993.
- Church News, June 26, 1993.
- "Church News, August 14, 1999.
- Veracruz in the News! Archived May 15, 2008, at the Wayback Machine., inficad.com, accessed 2008-03-14.
- "Six new stakes created; first one in Philippines," Ensign, August 1973, p. 78.
- Orson Scott Card, "It's a Young Church... In Mexico" Ensign February 1977, p. 17.
- "Chapter 5: The Orchard Years", Personal History of Claudious Bowman, Jr. and his wife Nelle, dublan.net, accessed 2008-03-14.
- Jason Swensen, "Mexico's Rich History preserved at newly dedicated records center", in Deseret News, April 20, 2017
- Deseret News, March 5, 1995
- Thomas W. Murphy, "Other Mormon Histories: Lamanite Subjectivity in Mexico", Journal of Mormon History 26 (Fall 2000):179–214.
- Church News, June 26, 1993 and June 20, 1997.