Preheat the oven to 350 degrees F.
Remove the tough outer leaves from the artichokes and cut the top quarter from each. Trim the stem ends as necessary. Cut in half lengthwise. As they are trimmed, place in a large non-reactive baking dish and toss with the lemon juice. Add the potatoes, onions, olive oil, garlic, salt and pepper, and toss to evenly coat the vegetables. Spread evenly and bake for 45 minutes to 1 hour, stirring occasionally. Add the tomatoes and stir well. Cook until the potatoes are tender, 10 to 15 minutes.
Remove from the oven and let cool. Add the olives and capers, and toss with the parsley and herbes de Provence. Adjust the seasoning, to taste, and add additional olive oil, if desired. Serve warm or at room temperature.
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