The Lychee Martini is a surprisingly full bodied drink with a vodka and fruit flavor blend. Learn to make a Lychee martini with a lychee garnish. So to make a Lychee martini you'll need equal parts of 2 ounces of vodka of your choice, and lychee juice which is essentially pureed lychees. These have been canned and pitted, very easy to use, puree that up. And at the very end were going to add a little bit of cassis for garnish.