Preheat oven to 375°F and line a muffin pan with liners.
In a small bowl, combine flour, brown sugar, and granulated sugar for the crumb topping. Pour in melted vegan butter and mix with a fork until crumbly. Set aside.
In a large bowl, whisk together flour, sugar, baking powder, and baking soda.
Add applesauce, melted vegan butter, almond milk, dairy-free yogurt, lemon juice, lemon zest, and vanilla extract. Mix gently until just combined. Do not overmix.
Divide the batter evenly into the muffin liners, filling about 3/4 full.
Sprinkle the crumb topping generously over each muffin, gently pressing it into the batter so it sticks.
Bake for 18–20 minutes, or until a toothpick inserted into the center comes out clean.
Let muffins cool in the pan for 5–10 minutes, then transfer to a wire rack to cool completely.
In a small bowl, whisk together powdered sugar and lemon juice until smooth. Drizzle over cooled muffins before serving.