Place the strawberry, mango, onion and orange juice into a large saucepan and bring to a boil over medium-high heat. Reduce the heat to low and cover the pot, allowing the fruits to simmer until soft, around 20 minutes.
Remove the soup from heat and, working in batches, carefully purée the mixture with a blender or food processor. Return the soup to the pot over medium-low heat. Remove 1/4 cup of the soup to a bowl and whisk in the cornstarch until smooth, then return to the pot while slowly whisking until the soup thickens, about 5 minutes. Remove from heat.
Chill for at least 3 hours.
Chill the soup completely and then add the milk and lemon juice.
Serve cold and garnish with fresh strawberry slices.