No. The Code of Canon Law states,
Among the forms of preaching the homily is preeminent; it is a part of the liturgy itself and is reserved to a priest or to a deacon; in the homily the mysteries of faith and the norms of Christian living are to be expounded from the sacred text throughout the course of the liturgical year. Whenever a congregation is present a homily is to be given at all Sunday Masses and at Masses celebrated on holy days of obligation; it cannot be omitted without a serious reason. (canon 767)
Furthermore, the instruction Inaestimabile Donum, issued by the Sacred Congregation for the Sacraments and Divine Worship and approved by Pope John Paul II on April 17, 1980 also condemns the practice you describe. Among the liturgical abuses condemned in the foreword of this document is "homilies given by lay people." Under the section on the Mass, subsection 3 states that "The purpose of the homily is to explain to the faithful the Word of God proclaimed in the readings, and to apply its message to the present. Accordingly the homily is to be given by the priest or the deacon."