Heat oil in medium skillet over medium-low heat. Add onion and jalapeño; sauté until tender, about 15 minutes. Add garlic; sauté 2 minutes. Season with salt. Remove from heat; cool.
Place avocados in blender. Add chicken broth, 4 tablespoons lemon juice and onion mixture. Puree until smooth. Transfer to large bowl. Stir in 2 cups water and lemon peel. Thin soup with more water, if desired. Season to taste with salt and pepper. Cover and refrigerate until well chilled, about 3 hours.
Meanwhile, mix shrimp, cucumber, chives, and 1 tablespoon lemon juice in medium bowl. Season with salt and pepper. Cover; refrigerate at least 1 hour and up to 3 hours. Ladle soup into bowls. Top with shrimp.