Cut the broccoli into florets. If the pieces are large, cut the stems in half. Rinse and drain them. Reserve the stems for another use. Drop broccoli into boiling salted water to cover. Bring to a boil and cook 2 minutes. Drain and run the broccoli briefly under cold water to cool. Drain again and chill. Cut the avocado in half. Peel each half and remove the pit. Cut each half into 8 lengthwise strips. Squeeze the lemon half over the strips to prevent discoloration. Arrange the broccoli and the avocado alternately on each of 4 serving plates. Blend the mustard, garlic, vinegar, pepper and oil, adding salt if needed, in a bowl with a wire whisk. Pour over the broccoli and avocado. Serve immediately.