Heat the oven to 350°F (175°C). Line a 12-cup muffin pan with paper liners. In a small bowl, stir the almond (or soy) milk with the apple cider vinegar; let it stand 5–10 minutes to lightly thicken.
Whisk together the flour, cane sugar, baking powder, and salt in a large mixing bowl. Add the softened vegan butter and blend on low speed (or rub in with fingertips) until the mixture looks like damp sand with no large butter pieces.
Whisk the applesauce, vanilla, and lemon zest into the soured milk. Pour this wet mixture into the sandy dry mix and stir with a spatula just until you no longer see dry flour. The batter will be slightly thick. Rest the batter for 5 minutes to hydrate for a softer crumb.
Divide the batter evenly among the liners, filling each about two-thirds full. Tap the pan twice on the counter to release any large air bubbles.
Bake for 18–20 minutes, until the tops spring back when gently pressed and a toothpick comes out with a few moist crumbs. Cool in the pan for 5 minutes, then transfer the cupcakes to a wire rack to cool completely before frosting.
Make the frosting: Beat the vegan butter on medium speed until pale and creamy, about 1 minute. On low speed, mix in about half of the powdered sugar. Add 2 tablespoons coconut milk, the vanilla, almond extract, and a pinch of salt; increase to medium-high and whip for 1½–2 minutes. Add the remaining powdered sugar gradually until fluffy. If needed, adjust with the remaining tablespoon of coconut milk, 1 teaspoon at a time. If your kitchen is warm, chill the frosting for 10 minutes before piping.
Pipe or spread the frosting onto the cooled cupcakes and finish with vegan sprinkles, if using.