Soften lahvosh by holding each side briefly under gently running cold water. Place lahvosh, sesame side down, between two damp, clean, kitchen towels. Let stand about 1 hour or until pliable.
Stir together cream cheese, artichoke hearts, pimiento, and oregano. Remove top towel from lahvosh. Spread lahvosh with cream cheese mixture to edges. Arrange prosciutto or ham over cream cheese layer. Arrange cheese slices in the center. Place lettuce leaf along one edge of cheese slices.
Roll from lettuce edge, using the towel to lift and roll the bread. Cover and chill, seam side down, for 2 to 24 hours. Trim ends of roll; cut roll into 1-inch-thick slices. Makes 14 slices.