1. In medium-sized bowl, stir lemon-flavor gelatin and unflavored gelatin until well mixed. Add 1 1/2 cups boiling water, stirring until gelatin completely dissolves. Stir in 3/4 cup cold water. Refrigerate, stirring occasionally, until mixture mounds slightly when dropped from a spoon, about 40 minutes.
2. Meanwhile, from lemon, grate 1 teaspoon peel and squeeze 2 tablespoons juice. In large bowl, with mixer at medium speed, beat softened cream cheese until smooth. Beat in sour cream, mayonnaise, vinegar, salt, grated onion, lemon peel, and lemon juice until blended. Set mixture aside.
3. Peel 3 cucumbers; cut each lengthwise in half; with spoon, remove seeds. Finely shred cucumbers to make about 2 cups. Place shredded cucumbers in colander to drain. Peel and remove seed from 2 avocados; mash avocados.
4. Stir gelatin mixture, shredded cucumbers, and mashed avocados into cream-cheese mixture. Pour mixture into 10-cup ring mold. Cover and refrigerate until set, about 4 hours.