Put the potatoes in a pot and cover with cold water by about 1 inch; add salt. Bring to a simmer and cook until fork-tender, about 8 minutes, then drain.
Meanwhile, cut the steak crosswise into 8 pieces and season with salt and pepper. Heat a large skillet over medium-high heat and add the olive oil. When hot, add the steak (in batches, if necessary) and cook until medium rare, 1 to 5 minutes per side, depending on the thickness. Transfer to a plate and tent loosely with aluminum foil.
Reduce the heat under the skillet to medium and add the bell peppers, onion, garlic, a splash of water and 1/4 teaspoon salt; cook, stirring often, until the vegetables are slightly soft, about 5 minutes. Add the tomato paste and cook, stirring, 1 minute. Increase the heat to medium high, add 3/4 cup water and simmer until the vegetables are tender, about 4 more minutes. Stir in the potatoes, parsley and lemon juice. Divide the steak among plates and serve with the vegetables and lemon wedges.