Combine vinegar, fresh lemon juice and Dijon mustard in bowl. Gradually whisk in oils. Season salad dressing to taste with salt and pepper. (Can be prepared 1 day ahead- cover and refrigerate.)
SALAD
Bring a pot of salted water to boil. Add green beans and cook until just tender, about 4 minutes. Drain and refresh with cold water, then drain again. (Can be prepared 1 day ahead. Cover and refrigerate.)
Preheat the oven to 400°F. Place bread slices on cookie sheet and bake until golden, about 5 minutes. Top bread with cheese. Bake until cheese softens and is heated through, about 10 minutes.
Meanwhile line plates with alternating Boston and red lettuce leaves. Mound green beans in center of leaves.
Cut avocado into thin slices and fan around beans. Place cheese croutes on one side of salad. Garnish with tomato wedges. Drizzle with vinaigrette and sprinkle with walnuts.