Does Deutero Isaiah Disprove the Book of Mormon?

Often the biggest attacks on the Book of Mormon end up becoming some of ts most amazing evidences.  Bible scholars hypothesize that Isaiah may have been written by two or even more authors.  According to scholars, Isaiah 1-39 was written by or recorded from the original Isaiah. but 40-55, or 66 was written after the Babylonian captivity.  This theory many stems from the mention of King Cyrus of Persia by name as king who would restore the people of Israel from captivity.  Scholars think it way too far fetched to believe any prophet could predict the future in such a specific manner.  There are several textual differences in style as well.  

So, if true, why would the second half of  Isaiah being written after the Babylonian captovity compketely disprove the Book of Mormon?  It would completely disprove the Book of Mormon quotes the second half of Isaiah yet Lehi left Jerusalem before the  Babylonian captivity and before deutero-Isaiah would have been written.