Divine Office Resources

Not sure of resources about the LOTH, but the set of books are on pre-pub.  

https://www.logos.com/product/33008/liturgy-of-the-hours

The Rule of St. Benedict with Notes in English edited by Timothy Fry has an Appendix which has some good stuff in it. Here's how it starts out:

Appendix 3

The Liturgical Code in the Rule of Benedict

From earliest times Christians have been conscious of the privilege and the responsibility of prayer. Paul exhorted the community at Thessalonica to “pray constantly” and to “give thanks in all circumstances” (1 Thess 5:17–18). In the theology of Luke’s Gospel, Jesus himself is portrayed as a man of prayer and as a teacher of prayer: “In these days he went out to the mountain to pray; and all night he continued in prayer to God” (Luke 6:12). It is not surprising, then, that in early Christian sources outside the New Testament we find an emphatic interest in prayer, personal and public. A survey of these sources will reveal four principal lines in the development of what we today call the Liturgy of the Hours or the Divine Office—an officially established pattern of common prayer (psalms, hymns, Bible readings, petitions) that punctuates the various hours of the day and night. With Juan Mateos, we may identify these four lines of development in the Liturgy of the Hours as follows:
1. times for prayer in the primitive Church;
2. the development of a “monastic tradition” of prayer-times in fourth-century Egypt;
3. the “cathedral tradition,” i.e., public prayer as celebrated in parochial or cathedral churches;
4. the rise of an “urban monastic tradition” of prayer-times.

Each of these four stages merits some attention.

[and then it goes on to give each of them some attention]

Saint Benedict Abbot of Monte Cassino, The Rule of St. Benedict in English with Notes, ed. Timothy Fry, electronic edition. (Collegeville, MN: The Liturgical Press, 1981), 379.

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Then there's an entry in The Modern Catholic Encyclopedia on "Liturgy of the Hours" which gives a bit about its history, insofar as it is known (it says the early history of it is obscure).

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More thorough background is available in these books listed in a bibliography in Twenty Centuries of Christian Worship (Library of Christian Worship: Volume 2), although alas none of these books is available in Logos:

Daily Prayer

Bradshaw, Paul. Daily Prayer in the Early Church. London: SPCK, 1981. A standard work that elucidates the origin and early history of the daily office of prayer from its Jewish background to the office of St. Benedict.

Guiver, George. Company of Voices: Daily Prayer and the People of God. New York: Pueblo Publishing Co., 1988. Deals with the history and content of daily prayer with an eye toward making the practice or prayer available to the common person.

Fisher, Dominic F., TOR. The Liturgy of the Hours. Petersham, Mass.: St. Bede’s Publications, 1987. A historical overview of the liturgy of the hours with practical guidelines for implementing the liturgy of the hours in the local parish.

Taft, Robert, S. J. The Liturgy of the Hours in East and West. Collegeville, Minn.: Liturgical Press, 1986. A scholarly investigation of the origins of the liturgy of the hours in the cathedrals and monasteries of both the East and the West. [Preview available on Google Books.]

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A search on Google Books for "liturgy of the hours" history will find you several other books with previews available that might help in your quest as well.