Place lettuce, cilantro, green chiles, tomatillos, green onions, and garlic in a blender. Puree, adding enough broth to make 3 cups liquid.
Heat oil in a 2- to 3-quart saucepan over medium-high heat. Add rice and saute until opaque, about 5 minutes. Add broth mixture and salt; bring to a boil. Cover and reduce heat to low. Simmer until rice is tender, 18 to 20 minutes.