That becomes one of the big debates. Who was the original author?
Certainly, as having been translated from Hebrew, we would like to believe that it is a manuscript that has been passed on, rewritten, etc. since Solomon himself.
Unfortunately, much of the linguistic style, the methods for describing the hierarchy of demons, and so forth point somewhat more toward medieval Europe as a period of origin rather than any old testament era.
While Hebrew apocryphal traditions are filled with various summoning methods and so forth, most of them can only be traced back to the medieval era, with little evidence existing that they date back much further than this. We must remember that within Hebrew tradition Solomon was eventually killed for turning away for Yahweh (god) for the very practice that is described with the Key of Solomon and the Lesser Key. This, to me, paints a rather unlikely picture of any real Hebrew mysticism growing up around his practices as they were already condemned by god and their religious traditions, and in turn casts a degree of skepticism over the Key and Lesser key's origins actually dating back to Solomon himself.
As mentioned above, the demons themselves are described very much in a medieval fashion, with legions and qualities and so forth that leave them seeming a blend of more ancient depictions of such spirits and more prevalent qualities that seem more in line with the various doctrines produced by the church at the time - the malleus malificarum and various demonologies actually produced so as to identify wtiches,demons, and those who consort with them.
Despite all of this, there are some interesting bits of high magic rooted within the texts, that offer you methods and practices that can be applied to a great many purposes. Also, while many of the claims of demons providing you with literal, secret gold, the ability to fly, and so forth are more than outlandish (I rather doubt the Golden Dawn would have so many legal troubles/divisions if they could just solve their problems with armies of demons), the insights provided concerning yourself, the world around you, and the nature of spirits/demons/angels themselves is definitely worthwhile gain should you decide to move forward with your evocation.