Combine the black rice, 1 tablespoon olive oil, 1/2 teaspoon salt and 1 1/2 cups water in a medium lidded saucepan or pot. Bring to a boil, cover, and cook over low heat until tender and the water is absorbed, 25 minutes. Keep covered and set aside.

Meanwhile, heat the coconut oil in a large nonstick skillet. Saute the cabbage and onion over medium-high heat until tender, 15 minutes. Stir in the lemon juice, tamari or soy sauce, and 1/2 teaspoon salt; continue to cook until the cabbage is soft and the liquid has more or less evaporated, another 5 to 10 minutes.

Off the heat, fold in the cooked rice and arugula. Divide between 4 plates and top with the avocado slices. Garnish with a drizzle of olive oil and sriracha.