What happened to the Book of the Law in the time of Josiah?
Edward F. Campbell Jr. says in 'A Land Divided: Judah and Israel from the Death of Solomon to the Fall of Samaria', published in The Oxford History of the Biblical World, that virtually all scholars agree the Book of Deuteronomy, or at least a good part of it (chapters 5-26 and 28 are often nominated), was the ‘Book of Law’ supposedly found in the temple during renovations in the time of King Josiah.
Was the Book of the Law lost for a long time that King Josiah never saw it before?
Not in the view of most biblical scholars. Tradition attributes the authorship of the Book of Law (Deuteronomy) to Moses, but scholars attribute the book, or most of it, to a source now known as the Deuteronomist, writing during the reign of King Josiah in Jerusalem.
Does this discovery of the Book of the Law mean that the location of the book was not known before?
This is apparently not the case. A very similar instance is reported in the Book of Jeremiah, demonstrating that this would not be the only case in which a document was hidden then 'found' by the priests in order to establish its antiquity and enable them to impress the king (who immediately saw through the ruse):
Jeremiah 36:19-23: Then said the princes unto Baruch, Go, hide thee, thou and Jeremiah; and let no man know where ye be. And they went in to the king into the court, but they laid up the roll in the chamber of Elishama the scribe, and told all the words in the ears of the king. So the king sent Jehudi to fetch the roll: and he took it out of Elishama the scribe's chamber. And Jehudi read it in the ears of the king, and in the ears of all the princes which stood beside the king. Now the king sat in the winterhouse in the ninth month: and there was a fire on the hearth burning before him. And it came to pass, that when Jehudi had read three or four leaves, he cut it with the penknife, and cast it into the fire that was on the hearth, until all the roll was consumed in the fire that was on the hearth.
In 'Ideas of Law and Legal Administration: a Semiotic Approach', published in The World of Ancient Israel (edited by R.E. Clements), page 193, Bernard S. Jackson agrees that the passage in Jeremiah suggests that the scroll found in the time of Josiah, just a few years earlier, had also been a ‘plant’. He says that Jeremiah has given us a vivid description of how it might have been done.
Did their ignorance of the presence of Book of the Law mean that nobody at that time cared to go inside the Temple to read from the Book of the Law?
This could hardly have been the case, especially for a period of hundreds of years, as supposed. All the scrolls were kept together, and if just one scroll had been placed in the wrong location in a sparsely furnished temple, its existence would quickly have been noticed.
How may we refute people who say that someone forged the book and put it there?
The scholarly position that Deuteronomy was written during the reign of King Josiah relies in part on the second, quite similar example in Jeremiah. This demonstrates a predeliction on the part of the priestly establishment to engage in deception and also a knowledge of how to carry out such a deception. Eliminating this example would remove a plank from the case that Deuteronomy was a recent forgery, although this would not necessarily mean that the book really dates all the way back to Moses.
The book's style is very similar to the style of set of books known as the Deuteronomic History, so it could help to show that the Deuteronomist was active even earlier than the reign of Josiah, although the consensus of modern scholars is that the evidence points to his reign. The late biblical Hebrew certainly places the book no earlier than the late monarchy, so there is a limit to how much earlier Deuteronomy can be dated.
