The Liturgy of the Hours is suggested here, but I don’t think it will ever gain a foothold in western lay spirituality without further adaptation. A monastic format simply will not develop, not when so many other alternatives are available.
[41.] For encouraging, promoting and nourishing this interior understanding of liturgical participation, the continuous and widespread celebration of the Liturgy of the Hours, the use of the sacramentals and exercises of Christian popular piety are extremely helpful. These latter exercises – which “while not belonging to the Liturgy in the strict sense, possess nonetheless a particular importance and dignity” – are to be regarded as having a certain connection with the liturgical context, especially when they have been lauded and attested by the Magisterium itself, [Cf. Pope Pius XII, Encyclical Letter Mediator Dei: AAS 39 (1947) p. 586; cf. also Lumen Gentium 67; Marialis Cultus 24; Directory for Popular Piety.] as is the case especially of the Marian Rosary. [Rosarium Virginis Mariae] Furthermore, since these practices of piety lead the Christian people both to the reception of the sacraments – especially the Eucharist – and “to meditation on the mysteries of our Redemption and the imitation of the excellent heavenly examples of the Saints, they are therefore not without salutary effects for our participation in liturgical worship ”.[Cf. Mediator Dei: AAS 39 (1947) p. 586-587]
Correct: prayer life and liturgy, when healthy, each inform a deeper and more fruitful experience of the other.