1. Line a large, rimmed baking sheet with paper towels. Put carrots in a large saucepan, cover with water and stir in 1 tsp. salt. Bring to a boil over high heat. Reduce heat to medium-low and simmer uncovered until carrots are just tender, 6 to 7 minutes. Fill a large bowl with ice water. Using a slotted spoon, remove carrots to bowl. Add onions to pan and simmer for 4 minutes. Adjust the heat as necessary to maintain a simmer.
2. Transfer cooled carrots from ice water to prepared baking sheet. Remove cooked onions to ice water; add ice to bowl as necessary. Continue to cook vegetables as follows, transferring cooked vegetables to ice water and draining on paper towels when cold: asparagus, 2 to 4 minutes; green beans, 4 to 5 minutes; sugar snap peas and baby lima beans, 2 minutes. (Vegetables can be cooked up to 5 hours ahead; cover and refrigerate. Bring to room temperature before continuing with recipe.)
3. Melt butter in a large skillet over medium heat. Add vegetables, including peas and artichoke hearts. Stir gently until heated through, about 5 minutes. Stir in tarragon and lemon juice and season with salt and pepper. Serve hot.