Lay people cannot give homilies, but there is a provision offered, as long as it does not “become a regular practice.”
[74.] If the need arises for the gathered faithful to be given instruction or testimony by a layperson in a Church concerning the Christian life, it is altogether preferable that this be done outside Mass. Nevertheless, for serious reasons it is permissible that this type of instruction or testimony be given after the Priest has proclaimed the Prayer after Communion. This should not become a regular practice, however. Furthermore, these instructions and testimony should not be of such a nature that they could be confused with the homily,[Cf. Ecclesiae de mysterio, Practical Provisions, art. 3 §2] nor is it permissible to
dispense with the homily on their account.