Did St. James write the Liturgy of St. James?
The short answer is probably not, but at one time it was ascribed to St. James by some.
It has also been ascribed to Saint Basil and to Saint John Chrysostom. In other words, we are not a 100% who composed the actual Liturgy of St. James.
The Liturgy of Saint James or Jacobite Liturgy is the oldest complete form of the Eastern varieties of the Divine Liturgy still in use among certain Christian Churches
It is based on the traditions of the ancient rite of the Early Christian Church of Jerusalem, as the Mystagogic Catecheses of St Cyril of Jerusalem imply. Forming the historical basis of the Liturgy of Antioch, it is still the principal liturgy of the Syriac Orthodox Church, Malankara Orthodox Syrian Church, Malankara Jacobite Syrian Church, Malankara Mar Thoma Syrian Church, Syriac Catholic Church, Syro-Malankara Catholic Church, Maronite Church. It is also occasionally used in the Eastern Orthodox Church and Melkite Catholic Church.
The Liturgy is associated with the name of James the Just, the "brother" of Jesus and patriarch among the Jewish Christians at Jerusalem. Saint James was martyred at the hands of a mob incensed at his preaching about Jesus and his "transgression of the Law" - an accusation made by the Jewish High Priest of the time, Hanan ben Hanan.
The historic Christian liturgies are divided between Eastern and Western usages. Among the Eastern liturgies, the Liturgy of Saint James is one of the Antiochene group of liturgies, those ascribed to Saint James, to Saint Basil, and to Saint John Chrysostom. Other Eastern liturgies include the Assyrian or Chaldean rites, as well as the Armenian and Maronite rites. The Byzantine liturgies attributed to Saint John Chrysostom and Saint Basil are the ones most widely used today by all Eastern Orthodox Christians and by the Eastern Catholic Churches in communion with Rome. - Divine Liturgy of Saint James
The Orthodox Wiki page on the subject of the Liturgy of St. James has this to say:
The Divine Liturgy of St. James is among the oldest Eucharistic services in continuous use. It is the ancient liturgy of the Church of Jerusalem and is attributed to the Apostle James the Just, the Brother of the Lord. It is often celebrated in Eastern Orthodox Churches on the feast of St. James (October 23).
History of the Liturgy
The general scholarly consensus is that this liturgy originated in Jerusalem during the late fourth or early fifth century. It quickly became the primary liturgy in Jerusalem and Antioch. Although it was later superseded in Jerusalem and Antioch by the Liturgy of St. Basil and the Liturgy of St. John Chrysostom, it had already spread to other areas of the Church. The oldest manuscript traditions are in Greek and Syriac, and there are also extant manuscripts in Armenian, Ethiopic, Georgian, and Old Slavonic.
One leading theory today is that of John Fenwick, who argues that the similarities between this liturgy and that of St. Basil demonstrate their respective developments from a common source, now lost, but which is best preserved in the Egyptian recension of the Liturgy of St Basil. Fenwick suggests that the Liturgy of St. James was composed by St. Cyril of Jerusalem c. 370.
The Catholic Encyclopedia seems to indicate that not so much that St. James is not the person who wrote the Divine Liturgy of St. James, as to where it originated:
The Rite of Jerusalem is that of Antioch. That is to say, the Liturgy that became famous as the use of the patriarchal church of Antioch, that through the influence of that Church spread throughout Syria and Asia Minor, and was the starting point of the development of the Byzantine rite, is itself originally the local liturgy, not of Antioch, but of Jerusalem. It is no other than the famous liturgy of St. James. That it was actually composed by St. James the Less, as first Bishop of Jerusalem, is not now believed by any one; but two forms in it show that it was originally used as local rite of the city of Jerusalem. There is a reference to the Cross among the prayers for catechumens--"Lift up the horn of the Christians by the power of the venerable and life-giving cross"--that is always supposed to be a reference to St. Helena's invention of the True Cross at Jerusalem in the early fourth century. If so, this would also give an approximate date, at any rate for that prayer. A much clearer local allusion is in the Intercession, after the Epiklesis: "We offer to thee, O Lord, for thy holy places which thou hast glorified by the divine appearance of thy Christ and by the coming of thy Holy Spirit" (these are the various sanctuaries of Palestine) "especially for holy and glorious Sion, mother of all Churches" (Sion, in Christian language, is always the local Church of Jerusalem. See JERUSALEM.) "and for thy holy Catholic and Apostolic Church throughout the whole world" (kata pasan ten oikoumenen, which always may mean, "throughout the whole Empire"). This reference, then, the only one to any local Church in the whole liturgy — the fact that the Intercession, in which they pray for every kind of person and cause, begins with a prayer for the Church of Jerusalem, is a sure index of the place of origin.
We have further evidence in the catechetical discourses of St. Cyril of Jerusalem. These were held about the year 347 or 348 in the Church of the Holy Sepulchre; it is obvious that they describe the liturgy known to his hearers there. Probst has examined the discourses from this point of view ("Liturgie des IV Jahrhunderts", Muster, 1893, 82-106) and describes the liturgy that can be deduced from them. Allowing for certain reticences, especially in the earlier instructions given to catechumens (the disciplina arcani), and for certain slight differences, such as time always brings about in a living rite, it is evident that Cyril's liturgy is the one we know as that of St. James. As an obvious example one may quote Cyril's description of the beginning of the Anaphora (corresponding to our Preface). He mentions the celebrant's versicle, "Let us give thanks to the Lord", and the answer of the people, "Meet and just". He then continues : "After this we remember the sky, the earth and the sea, the sun and the moon, the stars and all creation both rational and irrational, the angels, archangels, powers, mights, dominations, principalities, thrones, the many-eyed Cherubim who also say those words of David: Praise the Lord with me. We remember also the Seraphim, whom Isaias saw in spirit standing around the throne of God, who with two wings cover their faces, with two their feet and with two fly; who say: Holy, holy, holy Lord of Sabaoth. We also say these divine words of the Seraphim, so as to take part in the hymns of the heavenly host" ("Catech. Myst.", V, 6). This is an exact description of the beginning of the Anaphora in the Liturgy of St. James.
We have, then, certain evidence that our St. James's Liturgy is the original local rite of Jerusalem. A further question as to its origin leads to that of its relation to the famous liturgy in the eighth book of the Apostolic Constitutions. That the two are related is obvious. (The question is discussed in ANTIOCHENE LITURGY.) It seems also obvious that the Apostolic Constitution rite is the older; St. James must be considered a later, enlarged, and expanded form of it. But the liturgy of the Apostolic Constitutions is not Palestinan, but Antiochene. The compiler was an Antiochene Syrian; he describes the rite he knew in the north, at Antioch. (This, too, is shown in the same article.) The St. James's Rite, then, is an adaptation of the other (not necessarily of the very one we have in the Apostolic Constitutions, but of the old Syrian rite, of which the Apostolic Constitutions give us one version) made for local use at Jerusalem. Then it spread throughout the - Liturgy of Jerusalem
For those desiring to read the Divine Liturgy of St. James in English, it may be found here.
For those desiring to follow the Divine Liturgy of St. James it can be seen on YouTube: Orthodox Divine Liturgy According to Apostle James
Both the Catholic Church and Orthodox Church admit that some traditions are not reliable historically. Some traditions are basically legend. That does not make them lies. This Liturgy has been ascribed or attributed to St. James by some, but that does not make the Church Fathers liars. This Liturgy simply originated at Jerusalem and thus the confusion.