In a small bowl whisk together the lemon juice, shallot, 1 tablespoon of the basil and the lemon zest.
While whisking continuously, pour in 1/4 cup olive oil.
Season the vinaigrette with salt and pepper and set aside.
Make the Salad:
Heat your grill to high.
Place potatoes in large saucepan and add enough cold water to cover. Salt the water heavily (it should taste like sea water) and bring to a boil. Boil just until almost tender, about 4 minutes.
Drain the potatoes and transfer them to a work bowl. Add 1 teaspoon basil and 1-1/2 tablespoons oil. Toss with salt and pepper.
Combine squash and bell pepper in large bowl; add remaining 1 teaspoon basil and 1-1/2 tablespoons oil. Sprinkle with salt and pepper; toss to coat.
Toss potatoes in a grill basket or, using tongs, carefully arrange them in a single layer on your grill.
Grill until tender, about 10 minutes (5 minutes per side if cooking directly on the grill. If using a basket give it a good shake every minute.)
Transfer the potatoes to a large bowl and set aside.
Repeat with the squash and bell peppers. (If cooking directly on the grill turn them a few times with tongs, being careful not to tear the squash.)
Transfer squash to the bowl with potatoes and the bell peppers to a cutting board. Cut the bell pepper strips into 1-inch bite sized pieces and add to the vegetable bowl.
Drizzle with the vinaigrette and toss. Season with salt and pepper.