Roll out each pastry sheet to 10-inch square. Cut each sheet into 4 squares. Using a small knife, score 1/2-inch border (do not cut through pastry) around inside edges of each square. Arrange squares on 2 rimmed baking sheets covered with parchment paper. Melt butter in large skillet over medium-high heat. Add mushrooms, 1/4 tsp salt and pepper to taste. Sauté until tender and lightly browned and liquid has evaporated. Combine sautéed mushrooms, asparagus, thyme, lemon peel, 1/4 tsp salt and black pepper. Mix in créme fraiche and Gruyere.
Position one rack in top third of oven and one rack in bottom third of oven and preheat to 400°. While oven heats, divide and mound filling on pastry squares leaving 1/2-inch plain border.
Bake tarts 12 minutes, reverse sheets. Continue to bake until crusts are puffed and golden and filling is cooked through, about 10 additional minutes.
Refrigerate any leftovers and reheat on baking sheets for 5 minutes at 400°.