Lay out 1 sheet of phyllo dough. Spray lightly with olive oil cooking spray. Repeat with 4 remaining sheets. Cut phyllo sheets into 6 pieces. Fit each section into a muffin cup. Bake for 10 minutes.
Remove plastic cover from spinach souffle and microwave on high for 5 minutes. Remove from microwave and stir in lemon juice, salt, and cayenne pepper. Divide spinach mixture into baked phyllo cups. Sprinkle feta cheese over spinach mixture. Return to oven for 6 minutes. Serve hot.