I used a green apple vodka that had a bit of a sour punch, so I didn't feel the need to add lemon juice - and then the simple syrup to balance the tartness, but you may want to if your apple liquor is more subtle.
Garnish your martini glass with an apple slice and serve.
Notes
If you are not serving your cocktails straight away, soak the apple slices in lemon-lime soda or ginger ale or slice when you make the drinks.
You can substitute apple cider for the apple juice, just be aware that because cider is cloudy and unfiltered, your finished cocktail will lack luster while still tasting great.