Preheat your oven to 375°F (190°C). Line a muffin tin with paper liners or lightly grease the muffin cups.
Zest and juice 1 lemon. You might need another lemon to get all the juice you need, depending on the size of your lemon.
In a large bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and poppyseeds.
In a medium bowl, whisk together the coconut milk, lemon juice, lemon zest, melted coconut oil, vanilla extract, and applesauce.
Pour the wet ingredients into the dry ingredients and mix until just combined. Be careful not to overmix; it's okay if there are a few lumps.
Gently fold in the raspberries.
Divide the batter evenly among the muffin cups, filling each about 3/4 full. If desired, sprinkle a little turbinado sugar on top of each muffin for a crunchy topping.
Bake for 18-22 minutes, or until a toothpick inserted into the center of a muffin comes out clean or with just a few crumbs attached.
Let the muffins cool in the tin for about 5 minutes, then transfer them to a wire rack to cool completely.