In Ludlow's terms, this is the eschatological remnant, the final gathering. The Lord's hand is set "the second time" because there are limited returns by the temporal remnants in historical time. This however, is in the end of days, and this becomes the final and complete gathering together of the people of God.
In the context of the presence of these passages in the Book of Mormon, it is important to remember Nephi's association of his people with those who are scattered to the isles of the sea. Thus for these early Nephites, this verse would have a very particular and immediate resonance.