For the crumble: Preheat the oven to 350 degrees F.
Heat a wok over high heat and melt 2 tablespoons butter. Add the apples and stir-fry 1 minute. Add the cinnamon and sugar and stir-fry until the apples caramelize, about 2 minutes. Add the lychees and raspberries, stirring carefully. Remove from the heat and divide among four 6-ounce ramekins.
In a medium bowl, rub together the 6 tablespoons chilled butter, flour and sugar until crumbly. Sprinkle generously over the fruit to cover. Place the ramekins on a baking sheet and bake until the topping is bubbling and golden brown, 20 to 25 minutes.
For the sauce: While the crumble bakes, add the strawberries, 1/4 cup reserved lychee syrup and the sugar to a small wok or saute pan and bring to a simmer. Simmer until the mixture becomes thickened and reduces slightly, about 5 minutes.
When the crumble is cooked, top with scoops of vanilla ice cream, the strawberry sauce and garnish with a sprig of mint.