Finely grate 1/2 tsp. zest from a lemon and then juice the lemon to yield 1/4 cup (if it yields less, juice the second lemon). In a large bowl, whisk the zest, juice, oil, mint, dill, 1/2 tsp. salt, and 1/8 tsp. pepper.
Trim the tips and all but about 1/2 inch of the greens from the carrots and then peel them. In a large pot fitted with a steamer insert, bring an inch of water to a boil over high heat. Have ready a large bowl of ice water. Lay the carrots in the basket of the steamer, cover tightly, and steam until crisp-tender, 4 to 5 minutes. Cool the carrots in the ice water for a few minutes; then lift them out and add to the dressing.
Steam the peas in the same pot until barely tender, about 3 minutes. Cool them in the ice water for a few minutes, drain, and add to the carrots. Stir to coat the vegetables in the dressing. Taste and add more salt, if needed.
Let the vegetables sit for at least 30 minutes and up to 1 hour, tossing occasionally. With a slotted spoon, transfer the vegetables to a serving platter. Serve chilled or at room temperature.
You can make the entire dish up to 1 hour in advance.