Heat oven to 425° F.
Mix the potatoes, oil, chili powder, 1 teaspoon salt, 1/4 teaspoon pepper, and thyme in a medium bowl. Transfer to a roasting pan and cook, stirring once, until crisp and golden brown, about 40 minutes. Remove the potatoes from oven, transfer to individual plates, and wipe the pan clean.
Heat broiler. Season the steak with 1 teaspoon salt and 1/2 teaspoon pepper. Place on the clean roasting pan. Broil the steak to the desired doneness, 3 to 4 minutes per side for medium-rare. Transfer to a cutting board and let rest 5 minutes before slicing.
Serve with the potatoes and lemon quarters.
Upgrade: Skirt steak is a quick-cooking, reasonably priced cut of beef. If you prefer a thicker, leaner piece, try boneless rib eye or strip steak and add 2 to 3 minutes of cooking time per side.