Muddle the oranges and blackberries in a shaker.
Combine the remaining ingredients with ice, shake to chill, pour into a Collins glass and garnish.
Blend 36 oz of canned lychee with 22 oz of triple sec.
The remaining purée will keep in the fridge for about a week.
Alternatively, use ½ oz of premade lychee syrup and ¼ oz of triple sec.