Alvarez was born in Arteaga, Coahuila to Lino Alvarez and Margarita Vasquez. In 1956, when they were living in Saltillo, the Alvarez family joined the LDS Church. Alvarez served as an LDS Church missionary in the West Mexican Mission from 1965 to 1967, spending a good part of his mission in Sinaloa.
Alvarez has a bachelor's degree in Education. He met his wife, Argelia Villanueva, when he was teaching at a small school in Piedras Negras, Coahuila. They were married in the Mesa Arizona Temple. Alvarez later taught at LDS Church schools in Mexico and Chile as well as seminary and institute classes. At the time of his call as a general authority, Alvarez was the Church Educational System Area Director for Mexico. Alverez was involved in establishing LDS Institutes of Religion at many of the major universities in Mexico.
While living in Chile, Alvarez served as a district president. He was president of the Mexico City South Mission from 1982 to 1985. He later served as a Regional Representative of the Twelve with responsibility over Nicaragua. He had also served as Regional Representative over the Monterrey and Saltillo regions of Mexico.
In 1992, Alvarez became a member of the Second Quorum of the Seventy. In this position, Alvarez served in the Central America Area Presidency. In 1997, Alvarez was released from the Second Quorum of the Seventy and as a general authority.
The Alvarezes have three children.
- “’85 Mexico Quake: Ruins Then, Greater Faith Today,” Ensign, June 1986, pp. 76–78.
- “New Area Presidencies,” Ensign, Sep. 1995, pp. 74–76.
- Church News, May 20, 2006; January 24, 2004
- “Elder Lino Alvarez Of the Seventy,” Ensign, Sep. 1992, p. 76
- 2008 Deseret Morning News Church Almanac (Salt Lake City, Utah: Deseret Morning News) p. 101