Prep your tools. Line two baking sheets with parchment. Set your oven rack in the center and preheat to 325°F (165°C).
Cream the butter and sweetener. In a mixing bowl, beat the softened butter with the powdered sweetener until light and fluffy, about 1–2 minutes.
Add the lemon zest, lemon juice, and vanilla; mix to combine.
Combine the dry ingredients. In another bowl, whisk almond flour, xanthan gum, and salt until evenly blended.
Make the dough. Add the dry ingredients to the butter mixture. Mix on low until a soft dough forms and there are no dry spots. The dough should be pliable and slightly tacky but not sticky.
Shape and chill. Divide the dough in half.
Roll each half into a log about 1.5 inches in diameter. Wrap tightly in plastic and chill for 45–60 minutes, or until firm enough to slice cleanly.
Slice. Using a sharp knife, slice the logs into 1/4-inch rounds. If any edges crumble, gently press them back together.
Arrange on prepared sheets, spacing about 1 inch apart.
Bake. Bake for 12–15 minutes, rotating the pan halfway through. The cookies are done when the edges are just turning golden and centers look set. Do not overbake.
Cool. Let cookies cool on the sheet for 10 minutes, then transfer to a rack.
They will firm up as they cool.
Optional glaze. Whisk the lemon juice into the powdered sweetener to make a thick but pourable glaze. Drizzle over cooled cookies and let set 20 minutes.