Cook asparagus in salted simmering water in saucepan until tender, 5 to 8 minutes. Drain; keep warm on serving platter.
Meanwhile, heat oil and garlic in small saucepan over low heat; cook, stirring occasionally, until garlic is tender and golden, about 8 minutes; be careful garlic doesn't burn. Pour into a small bowl.
Add lemon juice, vinegar, salt, pepper and rosemary to garlic mixture; mix well. Pour over warmed asparagus. Serve.