This issue has been very clearly dealt with by Church authority. First, the Code of Canon Law states that the homily “is reserved to a priest or deacon” (CIC 767). The General Instruction of the Roman Missal goes further in its instruction to expressly exclude lay persons:
The homily should ordinarily be given by the priest celebrant himself. He may entrust it to a concelebrating priest or occasionally, according to circumstances, to the deacon, but never to a lay person. (GIRM 66, emphasis added)
Finally, the Congregation for Divine Worship and the Discipline of the Sacraments, in its instructional document Redemptionis Sacramentum, specifically names “pastoral assistants” and those who assume that function, as well as any other lay person, as those prohibited from preaching the homily:
The prohibition of the admission of laypersons to preach within the Mass applies also to seminarians, students of theological disciplines, and those who have assumed the function of those known as “pastoral assistants" ; nor is there to be any exception for any other kind of layperson, or group, or community, or association. (RS 66, emphasis added).
This issue looks “black and white” to me.