Melt 1 teaspoon butter in a medium nonstick skillet over medium-high heat. Add onion, celery, and thyme; sauté 5 minutes or until tender. Add peas, broth, sugar, and salt, and bring to a boil. Reduce heat, and simmer 15 minutes or until peas are tender.
Stir in 1/2 teaspoon butter, lettuce, and parsley. Remove from heat, and sprinkle with pepper.