Heat water to boiling in 2-quart sauce-pan. Add rice; reduce heat to low. Cover and simmer about 20 minutes or until water is absorbed. Cool slightly. Refrigerate about 30 minutes or until chilled. Stir vinegar, lemon peel, sugar and salt into chilled rice.
Cut and discard center ribs from romaine leaves. Cut leaves into strips, about 5 inches long and 3/4 inch wide. Mix mayonnaise, lemon juice and ginger; spread on each romaine strip.
Spoon about 1 tablespoon rice mixture over each strip to within 1 inch of 1 end. Place 3 or 4 vegetable strips on center of each romaine strip. Roll up; secure with toothpick. Top each with 1 shrimp. Refrigerate at least 2 hours before serving.