On July 12, 1971, Lucker was appointed Auxiliary Bishop of St. Paul and Minneapolis and Titular Bishop of "Meta" by Pope Paul VI. He received his episcopal consecration on the following September 8 from Archbishop Luigi Raimondi, with Archbishops Leo Binz and Leo Byrne serving as co-consecrators. In addition to his episcopal duties, he served as pastor of St. Austin's Church in Minneapolis (1971–74) and of the Church of the Assumption in St. Paul (1974–76). While at the Church of the Assumption, he also served as director of the Archdiocese's Liturgy Office. Lucker was named the second Bishop of New Ulm on December 23, 1975. His installation took place on February 19, 1976 at the Cathedral of the Holy Trinity in New Ulm. During his 25-year tenure, Lucker earned a reputation as one of the most progressive Catholic bishops in the country. He was a pioneer in the national movement to reform Catholic education, helping the nationwide development of the Confraternity of Christian Doctrine and the National Conference of Diocesan Directors. In 1989, he engaged in a public disagreement with Cardinals Joseph Ratzinger (later Pope Benedict XVI) and John J. O'Connor over the state of catechesis in the United States. During a meeting in Rome, Ratzinger allegedly said, "The developments in catechesis in the post-conciliar period, to a large extent, [have] been turned over to the so-called professional. This, in turn, has led to an excess of experimentation...making it all the more difficult to recognize that of the Gospel." O'Connor was reported to have said, "Basically confusion and diversity in catechetical materials have left an entire generation in a state of ambiguity. Some bishops are bludgeoned into compliance...and some bishops are browbeaten by directors of religious education so that bishops' feelings of inadequacy are heightened." In response, Lucker declared, "If what the two cardinals say is true, then there is no catechetical renewal and we have to go back to the '50s. Or, if it is not true, then we have an enormous communications problem with our own bishops and with many other people." The following year, he again criticized Cardinal Ratzinger after the Vatican announced it would give the world's bishops five months to express concerns about its draft of a universal catechism for adults; Lucker said, "A textbook is not the center and the focus of catechesis."