1. Preheat the oven to 350°F | 175°C and adjust the oven rack to the top third of the oven. In a bowl, toss about half the tomatoes gently — but well — with the 2 tablespoons olive oil, the sugar, and a couple of pinches of salt. Arrange them in a single layer, cut side up, on a rimmed baking sheet.
2. Bake, without stirring, until the tomatoes shrink a bit and start to caramelize around the edges, 45 to 60 minutes. Set aside to cool.
3. In the meantime, toast the caraway seeds in a dry skillet until fragrant. Transfer to a mortar and crush with a pestle. Add the garlic clove and a pinch of salt and mash into a paste. Work in the harissa, then the lemon juice, and gradually the remaining ⅓ cup olive oil.
4. When ready to serve, gently toss the roasted and raw tomatoes in a large bowl with about half of the harissa oil and the lettuce. Taste and season with a bit more salt, if needed. Serve topped with a little strained yogurt and the remaining harissa oil on the side.