Preheat the oven to 350°F. Add paper lines to a 12-cavity muffin pan or lightly spray the pan with cooking spray.
Shred the summer squash using the large holes on a shredding blade with a food processor. Alternately, you can use the large holes on a box grater. Wrap the shreds in a clean dish towel and wring them out over the sink, squeezing out as much liquid as possible. Measure 1 ½ cups of shredded squash and set aside.
In a medium mixing bowl, whisk together the flour, baking powder, and salt until well combined.
In a large mixing bowl, whisk together the sugar, milk, lemon zest, lemon juice, oil, and vanilla.
Pour the dry ingredients into the wet ingredients and stir until just combined. No white flour should remain visible, but a few lumps are fine and expected.
Add the shredded squash and stir until evenly distributed.
Transfer the batter to the prepared muffin pan. I like to use an ice cream scoop with a lever to evenly distribute the batter. Fill up each cavity to the top.
Bake for 25-28 minutes until a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for about 10 minutes before removing them to a cooling rack and continuing to cool completely.