Add lime juice, Cointreau, tequila, and apple cider to a cocktail shaker filled with ice. Shake until combined, about 15 seconds.
Rim glass with cinnamon sugar by running a lime wedge around the outer lip of your coupe glass. Slowly dip the rim into a wide bowl or plate filled with cinnamon sugar. Shake off any excess.
Strain shaker into coupe glass. Garnish with cinnamon sticks and apple slices, if using.
