Heat oven to 425°F (220°C). Put lentils and water in a saucepan. Bring to a boil, reduce to a gentle simmer and cook uncovered for 20–30 minutes, adding hot water if needed to keep them submerged. Start tasting at 20 minutes.

Meanwhile toss carrot pieces with 1 tablespoon oil, cumin, 1/4 teaspoon salt and pepper. Spread on a rimmed sheet pan and roast 20–25 minutes, turning once, until tender with lightly browned edges.

When lentils are tender but hold their shape, drain thoroughly. Spread in a shallow bowl and allow lentils and carrots to cool for about 10 minutes, until warm rather than steaming. Do not leave them out for hours.

Whisk remaining 2 tablespoons oil, lemon juice, mustard, garlic and remaining salt in a bowl. Stir in red onion so it softens slightly in the dressing.

Toss lentils and carrots with dressing. Fold in cucumber and parsley just before serving. Taste and add lemon or a little salt only if needed. Serve four meal-size portions, or divide into smaller side portions and adjust nutrition accordingly.