Preheat the oven to 350°F (175°C), and adjust the oven rack to the top third of the oven.
Place half the tomatoes in a bowl and toss along with the olive oil, sugar, and salt. Arrange them in a single layer, cut side up, on a rimmed baking sheet. Bake, without stirring, until the tomatoes shrink a bit and start to caramelize around the edges, 45 to 60 minutes. Set aside to cool.
When ready to serve, gently toss the roasted and raw tomatoes with a bit of chive or lemon oil, most of the almonds, the capers, the mozzarella, and the lettuce. Taste and season with a bit more salt if needed.
Serve topped with the remaining almonds, and any herb flowers you might have.