Stir together lemon juice and 1/2 tsp salt in small jar. Add oil, cover, and shake to blend.
Slice zucchini lengthwise as thinly as possible, using a mandoline or very sharp knife. Spread slices on platter and drizzle with lemon mixture. Tilt platter to evenly coat slices. Cover with plastic wrap and marinate at room temperature for 30 minutes to one hour.
Alternate zucchini and avocado slices on individual salad plates, slightly overlapping each slice. Sprinkle with pistachio nuts. Season with salt to taste, garnish with lemon thyme and serve.