Cut a thin slice from the top of each tomato. (If desired, cut a thin slice from bottoms of tomatoes so they stand upright.) With a small spoon or small lemon baller carefully hollow out the tomatoes. Line a baking sheet with paper towels. Invert tomatoes on the towels. Let stand 30 minutes to drain.
Meanwhile, for filling, in a food processor bowl combine avocado, cream cheese, pesto, and lemon juice. Cover; process until smooth. Spoon filling into a pastry bag fitted with a large plain round or open star tip.
Place tomatoes, open sides up, on a serving platter. Pipe filling into the tomato cups. Serve immediately or cover loosely and refrigerate up to 4 hours before serving. Sprinkle with snipped basil before serving. Makes 30 appetizers.