Is it ever appropriate for lay persons to vest in an alb and cope when they are called upon to preside at a celebration of the Liturgy of the Hours in the absence of a priest or deacon?
The introduction to the Liturgy of the Hours (no. 255) states:
The priest or deacon who presides at a celebration may wear a stole over the alb or surplice; a priest may also wear a cope. On greater solemnities the wearing of the cope by many priests or of the dalmatic by many deacons is permitted.
At more solemn celebrations of the Liturgy of the Hours, therefore, the dalmatic is worn by the deacon and the cope by the priest. The cope is also prescribed for the priest for processions and other services during the celebration of the Eucharist (General Instruction of the Roman Missal, number 303). The cope and humeral veil are worn by the priest or deacon when giving the blessing at the conclusion of the adoration of the exposed blessed sacrament in the monstrance (Holy Communion and Worship of the Eucharist Outside Mass, no. 92).
The vesture of lay persons who, in the absence of a priest or deacon, lead the Liturgy of the Hours is not explicitly addressed by the introduction to the Liturgy of the Hours. However, the cope is never prescribed for lay vesture in any of the other rites. Lay persons who lead celebrations of eucharistic adoration in the absence of a priest or deacon "wear either the liturgical vesture that may be traditional in their region or attire that is in keeping with this ministry and has been approved by the Ordinary (Holy Communion and Worship of the Eucharist Outside Mass, no. 20). Likewise, lay persons who preside at Sunday Celebrations in the Absence of a Priest wear "vesture that is suitable for his or her function or the vesture prescribed by the bishop" (Sunday Celebrations in the Absence of a Priest, no. 24).
While it is the role of the bishop to prescribe suitable vesture for those who lead celebrations of the Liturgy of the Hours, there appears to be no precedent in the post-Conciliar liturgical books for a lay person to be vested in a cope.