In a large bowl, combine strawberries, blueberries, and grapes. Peel lemons with a vegetable peeler, then stack the pieces of peel and cut them into fine julienne strips. Add them to the fruit.
Squeeze the lemons and combine their juice (you should have about ⅔ cup) in a small bowl with honey. Pour over the fruit and toss well to combine. Garnish with shredded basil and serve in small dessert bowls.