Bring the brown rice and water to a boil in a saucepan over high heat. Reduce the heat to medium-low, cover, and simmer until the rice is tender and the liquid has been absorbed, 45 to 50 minutes; remove from heat and allow to cool, fluffing occasionally with a fork.
Toss the avocado and lemon juice together in a large bowl. Add the tomatoes, cucumber, onion, feta, olives, mint, olive oil, lemon zest, garlic, salt, and pepper to the bowl; lightly toss the mixture until evenly combined. Fold the cooled rice gently into the mixture. Serve immediately or chill up to 1 hour; the salad does not last well for more than a day as the tomato and cucumber begin to release their juices and the salad becomes watery.