Preheat the oven to 425°F. Line a baking sheet with parchment paper and add the grapes to the baking sheet. Drizzle the olive oil over the top and sprinkle with the salt and pepper. Roast for approximately 20-25 minutes. Remove from the oven. Set aside.
In a medium cast-iron skillet, heat the olive oil over medium-low heat. Add the squash blossoms to the skillet, season with salt and pepper, and cook on both sides for 3 minutes total. Remove from the heat.
Put the lemon juice, honey, and olive oil in a small bowl. Season with salt and pepper and whisk to combine. Set aside.
Add the arugula to individual bowls. Arrange the grapes and squash blossoms on top of the arugula. Drizzle with the dressing and sprinkle the goat cheese over the top. Season with freshly ground black pepper, if desired. Serve immediately.