Pat black-eyed peas with a paper towel to remove excess water.
Mix peas, onion, peppers, and garlic in a bowl with salt, marjoram, dried parsley, black pepper, and cayenne pepper. Pour in enough olive oil and lemon juice to reach below the top layer of black-eyed peas. Adjust seasonings to taste. Cover and refrigerate, 8 hours to overnight.
Squeeze lemon juice over the top of the salad just before serving and garnish with fresh parsley.