One does not have to be a priest or deacon to lead the Liturgy of the Hours—provided that a priest or deacon is not present. Non-clerical religious have been doing it for centuries. If a priest or deacon is present, he should lead.
Furthermore, while a layperson can lead the Liturgy of the Hours, he should do it from his pew—not from the presidential chair. Nothing should be done that would blur the role of the laity with that of the priest. There is no reason for the lay leader to sit in the chair that is reserved for the priest-presider or to stand at the altar.