Preheat an oven to 350 degrees F (175 degrees C). Roll out and separate the crescent roll dough on a large baking sheet.
Mix together the cream cheese and butter in a bowl until well blended. Stir in the shredded chicken, mushrooms, and lemon pepper. Fill the crescent rolls with a tablespoonful of the chicken mixture. Roll each piece up beginning with the wide end; press and seal the top of the rolled dough. Brush the rolls with butter, then roll them in the crushed croutons. Return the coated rolls back to the baking sheet.
Bake in the preheated oven until golden brown, about 20 minutes.
Heat the drippings in a large skillet over medium-high heat. Stir in the onion and wine; cook and stir until most of the wine has evaporated, about 5 minutes. Pour in 1 cup of chicken stock and continue to cook and stir until the sauce has reduced by half, about 15 minutes. Reduce heat to low. Mix the cornstarch and remaining 3 tablespoons of chicken stock in a small bowl. Stir the cornstarch mixture into the skillet until thickened, about 5 minutes. Season with salt and pepper.
Spoon the hot gravy over the chicken rolls before serving.