Isaiah is a prophetic book written by Isaiah the prophet that apppears in the Old Testament section of the Bible. It contains prophecy that relates to the times that the Left Behind books deal with.
Isaiah 65:17-25 prophesies about both the "new heavens and new earth" (in verse 17) and the Jerusalem that appears in the Millennial Kingdom (in the following verses). These both appear in the Left Behind book "Kingdom Come". Verse 20 is interpreted by the writers of the series as the "naturals" living in that time period being able to live long lives as believers while unbelievers will die at the age of 100.