Bring brown rice and water to a boil in a saucepan over high heat. Reduce the heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes. Remove from heat and allow to cool, fluffing occasionally with a fork.

Toss avocado and lemon juice together in a large bowl. Add tomatoes, cucumber, feta, onion, olives, mint, olive oil, lemon zest, garlic, salt, and pepper to the bowl; lightly toss the mixture until evenly combined.

Fold 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.