Place red onion in a bowl of ice water; let stand 30 minutes. Drain. Return to bowl, add the lemon juice and sugar; set aside.
In small bowl combine rosemary, thyme, 1/2 teaspoon salt, and pepper; rub mixture and 1 teaspoon oil into steak. (Let stand while potatoes cook.) Place potatoes in a large saucepan; cover with cold water. Bring to boil, then reduce to simmer. Place a mesh colander or steamer over pan; add green beans, and cover. Cook 5 minutes.
Remove colander, and transfer beans to a plate to keep warm. Continue cooking potatoes until soft when pierced with a knife, about 15 minutes total. Drain, reserving 3/4 cup cooking water. Return potatoes to pan. Add remaining 1 tablespoon oil and 1/4 teaspoon salt, plus 1/2 cup cooking water; mash the potatoes, adding more reserved water, if necessary.
Meanwhile, heat broiler with rack 4 inches from heat; broil flank steak to medium-rare, about 3 minutes per side, depending on thickness. Let rest 5 minutes; slice across grain into 1/8-inch slices. Arrange on a dinner plate; serve with potatoes, pickled onion, and green beans.