Heat oil in a large saucepan over medium heat. Cook and stir rice in hot oil until golden brown, 3 to 5 minutes; add onions and garlic and cook until the onion is softened, 5 to 7 minutes more.
Pour vegetable broth and water into the saucepan; bring to a boil, reduce heat to low, place a cover on the saucepan, and cook rice at a simmer until tender and the liquid is absorbed, 10 to 15 minutes. Fluff rice and cook 1 to 2 minutes more.
Scoop rice mixture into lettuce leaves. Season with soy sauce or lime juice, as desired.