1 pound white asparagus, trimmed, peeled, and cut into 2-inch pieces
1 pound green asparagus, trimmed and cut into 2-inch pieces
3/4 stick (6 tablespoons) unsalted butter, cut into tablespoon pieces
1/2 cup finely chopped shallots (2 large)
1/4 pound fresh morels, cleaned and halved lengthwise if large
1 tablespoon chopped fresh tarragon
1/2 teaspoon salt
1/4 teaspoon black pepper
1 tablespoon fresh lemon juice
Garnish: chopped fresh tarragon
Cook white and green asparagus separately in a 5- to 6-quart pot of boiling salted water, uncovered, until just tender, about 5 minutes for white asparagus; about 3 minutes for green asparagus.
Transfer asparagus with a slotted spoon to a colander and rinse under cold water (to stop cooking), then drain again. Pat dry.
Heat 3 tablespoons butter in a 12-inch heavy skillet over moderately high heat until foam subsides, then sauté shallots, stirring, until golden brown, about 2 minutes. Add morels and sauté, stirring frequently, until tender, about 5 minutes. Add asparagus, tarragon, salt, pepper, and remaining 3 tablespoons butter and sauté, stirring, until heated through, about 3 minutes. Remove from heat and stir in lemon juice. Serve immediately.