In a medium bowl, combine oats with 3/4 cup water. Let stand while you prepare remaining ingredients.
Put lemon juice in another bowl. Peel 1 apple, then cut out 8 very thin slices. Turn slices in lemon juice and lift out; set aside. Peel and coarsely shred remaining apples into lemon juice; mix immediately.
Stir apples, nuts, syrup, and coconut into oats. Divide among 4 bowls. Serve with yogurt if you like; garnish with apple slices.
*Agave syrup (also called agave nectar) is a sweetener made from the juice of the agave plant. Find it at well-stocked grocery and natural-food stores.
Make ahead: In step 1, combine oats with 1 1/2 cups water; chill at least 2 hours and as long as overnight, then drain (oats will be fuller-textured than when short-soaked).
Note: Nutritional analysis is per serving.