score:5
No. Luther is not known to have read the First Epistle of Clement. In fact it is certain that he did not read it.
Luther was, in general, very well read in the Church Fathers; and he would have known, from Eusebius and others, that such an epistle had once existed. However it had long since disappeared, and no copies were known to exist. It was only in 1628, more than 70 years after Luther's death, that Western scholars were able to read it. This happened when Patriarch Cyril I, of Constantinople, presented King Charles I of England etc. with a copy of the Bible containing, separately at the back, a copy of Clement's Epistle. This became known as the Codex Alexandrinus, because it had been found, a few years earlier, in Alexandria. The Patriarch had intended it to go to King James, but he died before it arrived. It was published by Patrick Young, the Royal Librarian.
Doctor Bell in his translation of the Familiar Discourses of Luther lists some, though not all, of the Early (and later) Fathers Luther was familiar with including a date when they were thought to have been active.
Athanasius of Alexandria (387)
Basilius Magnus and Gregorius (380)
Ambrose of Milan (380)
Aurelius Prudentius (380)
Austin of Hippo (430)
Beda, a Benedict in England (737)
Cyprian of Carthage (259)
Cyril of Alexandria
Chrysostom of Constantinople (420)
Gregory I, Pope (511)
Hierem, eldest of Striden (522)
Irenaeus of Lyon (175)
Polycarpus, tutor to Irenaeus (1&5)
Nicolas de Lyra (330)
Origen of Adomantz (261)
Philo the Jew (50)
Josephus (100)
Ignatius of Antioch (111)
Prosperus of Rogen (460)
Sedulius (430)
Tatianus the Heretic (170)
Thomas Aquinas (1274)
Bonifacius of Mentz (755)
Bernard of Cistern (1140)
Hugo Parisiensis (1130)
Anselmus (1110).
Further detail is included in Staniforth Maxwell's Early Christian Writings and the Apostolic Fathers. This link is to a preview. The pages are not numbered but it is on the twelfth page.