I remember how surprised I was when I discovered other churches where "God's Peace" was said. In Lutheran, Methodist, Presbyterian, Episcopalian, Catholic and other liturgical churches, the Passing of the Peace usually takes place after the Lord's Prayer. Congregants are invited to turn to each other, shake hands and say "the Peace of the Lord be with you" or some variant thereof.
In the letters of St. Paul there are several references to greeting one another with "a holy kiss" (Rom 16:16; 1 Cor 16:20; 2 Cor 13:12; 1 Thess 5:26; 1 Pet 5:14). Some view this as a sign of reconciliation, some as a simple blessing, some as a recognition of the Christ within our neighbor.
According to Joseph Jungman, a Jesuit historian of liturgy, this ritual was the Christian appropriation of a secular practice when a kiss was the sign of initiation into a fraternity or society. Thus the Christians took a secular practice and incorporated it into the sacrament of initiation where it took on added meaning. While the practice died out in secular society as culture changed, its meaning in the Christian community continued, although it degenerated to a tap on the cheek and ultimately to a handshake.
I would say that by using it as a signal of membership, the OALC has preserved its secular nature very well.