Cut avocado lengthwise around middle; remove pit with a knife blade; twist avocado to separate halves; scoop out halves with a spoon; cut enough into 1/4" pieces to make 1/4 cup toss with 1 tsp. of the lemon juice and set aside. Cut the remaining avocado into large chunks and combine with remaining 2 tsp. lemon juice; transfer to the bowl of a food processor.
Heat the oil in a large saucepan over medium heat; add the leeks and cook until soft, 4 minutes. Add the tomatoes, corn, garlic, and pepper; cook and stir until everything is hot. Add half of the vegetables to the avocado in the food processor; process until smooth.
Add the stock and soy milk to the remaining vegetables in the saucepan and bring to a full boil. Stir in the pureed avocado mixture; divide into 4 soup plates; top each with some of the reserved finely chopped avocado.