In many cases, the spiritual meaning of "own," both as a verb and as an adjective, is relatively literal. When people are described as the "Lord's own," however, it specifically means those people who know Him and have His Word. This has taken various forms since the dawn of humanity; in the prehistoric church known as the "Most Ancient Church" the Lord's truth - the direct expression of His love - flowed into people directly. In the Ancient Church the Lord's Word was recognized in nature and in the form of deeply representative stories, some of which were passed on to us in the early chapters of Genesis. Among the Children of Israel the Lord's Word was expressed through the Ten Commandments, the laws of Moses, the very history of the nation of Israel and the various psalms and prophecies. The early Christians had those stories along with the teaching and inspiration of Jesus himself. We now have the whole Bible, including the teachings of Jesus, and can understand the Bible's true meaning thanks to the works of Swedenborg.
Each of these churches, then, was at some point the "Lord's own."
(References: Arcana Coelestia 8768)