The trick to making sure that the bottoms of your pies are crispy and cooked through is pre-heating the sheet pan first. Because the filling is pre-cooked, the oven is set to a high temperature to speed up the cooking time.
For the pies: Place a large sheet pan on a rack in the center of the oven. Preheat the oven to 450 degrees F.
Heat the oil in a large skillet over medium-high heat. Add the mushrooms, 1/2 teaspoon salt and 1/4 teaspoon pepper and cook, tossing the mushrooms occasionally, until they soften and turn golden, 2 to 3 minutes. Remove from the heat and add the cream cheese. Stir until the cheese is melted. Fold in the chicken, mustard and chives.
Lightly flour a work surface and roll the pastry into an 11-inch square. Cut the pastry in half. Divide the chicken and mushroom mixture in half and place each half on one end of each rectangle of pastry, leaving a 1/2-inch border on all sides.
Brush the border with the egg and fold over the other half of the puff pastry. Use a fork to crimp and seal the edges. Brush the tops of the pies lightly with the egg. Transfer the pies to the hot baking sheet and bake until deep golden brown, about 15 minutes.
Meanwhile, for the salad: Whisk together the lemon juice, oil and mustard in a large bowl. Season with a pinch of salt and pepper. Fold in the thinly sliced onions and toss occasionally to soften, 5 to 10 minutes.
When ready to serve, toss the lettuce and chives into the dressing.