Preheat oven to 325 degrees F (165 degrees C). Grease a loaf pan.
Mash thawed raspberries in a bowl with a fork; press raspberries through a sieve to remove seeds. Mash banana in another bowl with a fork.
Combine flour, cinnamon, baking soda, salt, and nutmeg in a bowl. Beat sugar, eggs, raspberries, banana, and vegetable oil in a bowl with an electric mixer set on low until smooth, 2 to 3 minutes. Stir flour mixture into raspberry mixture until batter is just moistened; stir in lemon extract. Pour batter into prepared loaf pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour. Cool in the pan for 10 minutes before removing to cool completely on a wire rack.
