The Book of Mormon talks about the 3 Nephites and how they are still roaming the earth today teaching the Gospel of Jesus Christ. If this is the case, then the church was never lost so the Church would not need to be restored by Joseph Smith, making the LDS church a false church.
The attempt to create a logical paradox that destroys the church fails. Given that the The Book of Mormon is where the 3 Nephites are introduced and what little we know of how they work is defined. Then it is only fair to look to see what it tells us about them for the purposes of this little logic puzzle.
Mormon 1:16 tell us
16 And I did endeavor to preach unto this people, but my mouth was shut, and I was forbidden that I should preach unto them; for behold they had wilfully rebelled against their God; and the beloved disciples were taken away out of the land, because of their iniquity.
The 3 Nephites are the beloved disciples mentioned as being taken away. God took them away due to the wickedness of the people. If they were taken away once, then the logical construction that requires that they never leave to hold the church in existence is shown to be false. After all if God took them away while there was a prophet like Mormon around, there is no way to make a case for them being around if things are so bad that will not call a prophet for them.
This makes it quite possible for the church to be lost and need to be restored. Just as it did happen with the coming forth of the Book of Mormon and the calling of Joseph Smith to be a prophet .