Preheat the oven to 180C/160C Fan/Gas 4.
Use your hands to mulch the egg whites, sugar, coconut, lime zest and juice in a bowl until they lightly come together.
With wet hands, press the mixture into a flat, square shape about 1cm/0.5in high.
Use a small upturned liqueur glass to cut out small rounds, and place on a lightly oiled or nonstick baking tray.
Bake for 12-15 minutes in the centre of the oven until very lightly golden, just touched with colour.
Cool the macaroons on a wire rack, and store in an airtight jar.