Combine the barley and water in a medium saucepan and bring to a boil. Reduce the heat to low and simmer for 40 to 50 minutes until all of the liquid is absorbed. Remove from heat and allow to cool slightly.
In a large bowl, whisk together the soy sauce, sesame oil, lemon juice, oregano, and lemon zest until well combined. Add the slightly cooled barley to the bowl and toss to coat.
Add the shelled edamame and arugula and toss gently to combine. To serve, divide the barley salad among four bowls and top with tofu and avocado slices.
*Hulled barley is barley in its most natural state, which means it needs to cook for quite a bit longer than pearl barley-1 to 1 1/2 hours longer. Pearl barley has the hull removed and is therefore less tough. Adjust your cooking time based on the variety you choose.