Once the chain of command is invoked, a lay person may preside at a liturgy:
25. Where there is a shortage of Priests and Deacons, the Diocesan Bishop can delegate laypersons to assist at Marriages, after a prior favorable vote of the Conference of Bishops and after the permission of the Apostolic See has been obtained. A suitable layperson is to be selected, who is capable of giving instruction to those preparing to be married and able to perform the Marriage liturgy properly.(cf. canon law 1111-1112) The layperson asks for the consent of the spouses and receives it in the name of the Church.(cf. canon law 1108)
The text cited in blue is from the English translation of The Order of Celebrating Matrimony © 2013, International Commission on English in the Liturgy Corporation. All rights reserved.