Break off asparagus ends at the point where the stems snap easily; discard ends.
In a large skillet, bring about 1 cup salted water to a boil and add the asparagus. Cover and simmer 5 to 6 minutes, or until just tender; drain.
Meanwhile, in a 10- by 6-inch baking dish, mix oil, lemon juice, garlic, Worcestershire sauce, salt, and sugar. Add hot asparagus, turning to coat the spears with the dressing. Cover and refrigerate 2 hours, turning once.
Arrange asparagus on a platter. Toss tomatoes with the dressing left in the baking dish and spoon over the asparagus.
