In a medium bowl, whisk together the flour, granulated sugar, baking powder, lavender, salt, and zest. Set aside.
In a large measuring cup or small bowl, whisk together the eggs, lemon juice, and vanilla. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or in a medium mixing bowl, using a handheld mixer), beat the butter on medium speed until creamy and pale, about 1 minute.
With the mixer on low speed, slowly stream in the egg mixture, mixing until fully incorporated and smooth.
On low speed, add the flour mixture in thirds, mixing until just combined.
Remove the bowl from the mixer stand (if using) and mix by hand to make sure no bits of flour or butter are hiding on the bottom of the bowl and the dough is thoroughly mixed.
Cover the bowl with plastic wrap and chill the dough in the refrigerator until firm, about 1 hour.
When ready to bake, position the racks in the middle and lower third of the oven and preheat the oven to 350°F (175°C). Line two baking sheets with parchment.
Put the confectioners' sugar in a small bowl.
Use a small ice cream scoop or a tablespoon to form the cookies (about 1 rounded tablespoon each).
Roll each one in the confectioners' sugar, coating it completely, and place on the prepared baking sheets, leaving 2 inches (5 cm) between the cookies to allow for spreading.
Bake the cookies for 10 to 12 minutes, rotating the pans halfway through and switching their positions, until lightly golden and puffed up.
Let cool completely on the pans on wire racks.
The cookies can be stored in an airtight container at room temperature for up to 3 days.