1. In a large bowl, whisk together the vinegar, corn syrup, oil, salt and pepper. Add the onion and black-eyed peas.
2. If using frozen lima beans, cook them in a large saucepan of boiling salted water until tender, about 5 minutes. Remove the beans with a slotted spoon and plunge them into an ice bath. Pat dry and add to the onion mixture. If using dried lima beans, drain the cooked and cooled lima beans, pat dry and add to the onion mixture. (The beans can be cooked in advance and stored covered in a refrigerator for up to 8 hours.)
3. Cook the green beans in boiling salted water until just tender, about 3 to 6 minutes. Drain and plunge into an ice bath. Pat dry and add to the salad along with the parsley. Toss well. Adjust the salt and pepper to taste.Serving Size: about 3/4 cup