In a large nonstick skillet with a lid, heat oil over medium. Add shallots and cook until they begin to color, about 3 minutes. Add mushrooms, season with salt and pepper, and cook, tossing occasionally, until mushrooms and shallots are tender, 3 to 5 minutes. Transfer to a bowl. Add lemon zest and tarragon; toss to combine.
In the same skillet, bring 2 inches of water to a boil. Add asparagus, season with salt, cover, and cook until asparagus is bright green and tender, 3 to 4 minutes (timing will vary depending upon thickness of asparagus). Add peas to skillet, and then drain.
Transfer to bowl with the shallots and mushrooms, add lemon juice, and toss to combine.