Position racks in the upper and lower thirds of the oven and preheat to 325 degrees F. Line 2 baking sheets with parchment paper. Pulse the pistachios in a food processor until finely ground but not powdery. Whisk the egg whites with the sugar, lemon zest, vanilla and salt in a large bowl until frothy. Stir in the ground pistachios, then stir in the coconut until completely combined.
Scoop heaping tablespoons of the coconut mixture onto the prepared pans. Bake, switching the pans halfway through, until the macaroons are golden, 25 to 30 minutes. Let cool 10 minutes on the pans, then transfer to a rack to cool completely.