Brush both sides of the salmon with 1 teaspoon lemon juice and sprinkle with salt and pepper, to taste. Set aside.
Warm 2 tablespoons oil in 2 separate skillets over medium-high heat. Add half of the onion and half the garlic to each pan. Season with salt and pepper, to taste, and saute until tender, about 5 minutes. Stir in the mushrooms and thyme into 1 pan and the spinach, lemon zest and remain lemon juice in the other pan. Stir the spinach until it wilts, then transfer it to a bowl and set aside. Saute the mushrooms until they are reduced and tender, about 5 minutes. Turn off the heat and stir in the sour cream. Set aside.
Trim the thinner ends of the salmon fillet so you have 4 pieces of even thickness. Unroll a pastry sheet on a lightly floured surface. Pass a rolling pin lightly over 2 or 3 times to seal the seams and lengthen slightly. Cut the pastry sheet into 3 equal strips, using the natural seams as a guide. Roll out the second puff pastry sheet to get 1 more strip. Save remaining puff pastry for another use. Lightly prick the 4 strips with a fork. Put 1 heaping spoonful of mushroom mixture on 1 half of each pastry, top with salmon, then layer with a heaping spoonful of spinach mixture. Wet the edges of the pastry with water and fold over the other half, pressing lightly and folding to seal the edges. Repeat with remaining pastry and filling. Cut 2 vents on the top of each pastry packet and arrange them on a parchment-lined baking sheet.
Bake until the pastry is golden and fish is just opaque in the center, about 25 to 30 minutes.
Transfer the pies from the oven to serving dishes and garnish with chopped parsley.