There does seem to have been a developing sense of divisions of the Hebrew scriptures in the Second Temple period, with 'the Law' and 'the Prophets' mostly settled, but further divisions were still up in the air.
The prologue of Sirach, written around 130 BC, mentions the Law, the Prophets, and 'the rest of the books of our fathers':
Many great teachings have been given to us through the Law and the Prophets and the others that followed them, and for these we should praise Israel for instruction and wisdom. Now, those who read the scriptures must not only themselves understand them, but must also as lovers of learning be able through the spoken and written word to help the outsiders. So my grandfather Jesus, who had devoted himself especially to the reading of the Law and the Prophets and the other books of our ancestors ... Not only this book, but even the Law itself, the Prophecies, and the rest of the books differ not a little when read in the original.
(Sirach prologue, NRSV)
Philo, writing in the first half of the first century AD, has the Law, the Prophets, as well as hymns, psalms, and wisdom literature:
And in every house there is a sacred shrine which is called the holy place, and the monastery in which they retire by themselves and perform all the mysteries of a holy life, bringing in nothing, neither meat, nor drink, nor anything else which is indispensable towards supplying the necessities of the body, but studying in that place the laws and the sacred oracles of God enunciated by the holy prophets, and hymns, and psalms, and all kinds of other things by reason of which knowledge and piety are increased and brought to perfection.
(Philo, On the Contemplative Life 3.25, Yonge's translation)
Josephus, around 95 AD, comes closet to providing us with the familiar idea of a threefold canon, in that he specifically numbers (but doesn't strictly identify) twenty-two books of a canon, including: the Law (five books), the Prophets (including History, thirteen books), and a final set of 'hymns' and 'precepts' (four books):
For we have not an innumerable multitude of books among us, disagreeing from and contradicting one another, but only twenty-two books, which contain the records of all the past times, which are justly believed to be divine. Of them five belong to Moses, which contain his laws and the traditions of the origin of mankind till his death. (This interval of time was little short of three thousand years.) But as to the time from the death of Moses till the reign of Artaxerxes king of Persia, who reigned after Xerxes, the prophets, who were after Moses, wrote down what was done in their times in thirteen books. The remaining four books contain hymns to God, and precepts for the conduct of human life. It is true, our history has been written since Artaxerxes very particularly, but has not been esteemed in the manner of authority with the former by our forefathers, because there has not been an exact succession of prophets since that time...
(Josephus, Against Apion 1.8, William Whiston translation)
The passage in Luke simply reflects the lack of a specific, closed canon at that time, and shouldn't be pressed too far as an explicit identification of a settled Hebrew "bible". Hence, there was no established label for sections beyond 'the Law' or 'the Prophets'.