To your rice cooker, add the oil, rinsed and drained rice, lemon pepper, and basil, set the rice cooker to Cook. You are NOT using the cover yet. Stir to mix the oil into the rice, and stir often as the cooker heats and the rice turns translucent. This will take 3-5 minutes once the the cooker comes up to temperature.
Now pour in the chicken stock, lemon juice, butter, and a pinch of salt as desired. If using the ponzu sauce, add that now as well. Give everything a stir to combine.
Cover with the lid, leaving the setting on Cook.
When the rice cooker switches to Warm setting, leave the cooker covered for 3-5 minutes, then turn off, fluff with a rice paddle.
Serve as a side dish with any meal.