Q. 1. Are lay persons allowed to present the homily at the Holy Mass on Sundays?
A. 1. Based on Canon Law # 764, the preaching of homilies is restricted to priests and deacons.
# 764 "Without prejudice to the prescript of can. 765, presbyters and deacons possess the faculty of preaching everywhere; this faculty is to be exercised with at least the presumed consent of the rector of the church, unless the competent ordinary has restricted or taken away the faculty or particular law requires express permission."
Lay persons are allowed to preach the homily at the Holy Mass under certain circumstances as stated in Canon Laws # 766 & 767.1
# 766 "Lay persons can be permitted to preach in a church or oratory, if necessity requires it in certain circumstances or it seems advantageous in particular cases, according to the prescripts of the conference of bishops and without prejudice to can. 767, §1."
# 767 §1. "Among the forms of preaching, the homily, which is part of the liturgy itself and is reserved to a priest or deacon, is preeminent; in the homily the mysteries of faith and the norms of Christian life are to be explained from the sacred text during the course of the liturgical year."