Prepare an ice-water bath. Bring a large saucepan of water to a boil over high heat. Add salt, return to a boil and add asparagus. Cook until just tender, drain asparagus, and immediately transfer to ice-water bath to cool. Drain from ice water and set aside.
Bring a large saucepan of water and lemon juice to a boil over high heat. Add artichokes and cook until tender, about 15 minutes; drain.
In a large skillet, heat 1 tablespoon butter over medium-low heat. Add shallot and cook until softened, about 1 minutes. Add asparagus, artichokes, peas, thyme, and 2 tablespoons water. Bring to a simmer and cook until heated through. Remove thyme sprigs, season with salt and pepper, and stir in chopped herbs. Add remaining tablespoon butter and swirl until melted. Serve immediately.