Bring the rice, 3 cups water, and a pinch of salt to a boil in a medium saucepan over medium heat. Reduce the heat to a gentle simmer, stir, cover, and cook until water is completely absorbed, 15 to 18 minutes. Remove from heat and let stand, covered, for 10 minutes.
Meanwhile, put the avocado, basil, lemon juice, oil, and 1/4 cup water in the jar of a blender and puree; season generously with salt and pepper. Add more water and puree until the mixture is the consistency of sour cream.
Fluff the rice with a fork and gently fold the green dressing into the warm rice. Taste and add more salt and pepper, if necessary. Serve immediately.