Place racks in upper and lower thirds of oven; preheat to 325°F. Whisk egg whites and sugar in a large bowl just until frothy. Whisk in lime zest and salt. Add coconut and fold to coat.

Drop heaping tablespoonfuls of coconut mixture onto 2 parchment paper-lined rimmed baking sheets. Bake, rotating pans halfway through from top to bottom and back to front, until golden brown, 18-22 minutes. Let cool on baking sheets. DO AHEAD: Macaroons can be made 1 day ahead. Store airtight at room temperature.