Green water means excess nutrients - too many fish, too few plants, too much feeding, organic material decaying in the pond, or a combination of any or all of the above. Address the cause and the symptom will take care of itself.
Your pond is just over 500 US gallons. To me the main thing lilies add to a pond is shade - they stay in the pot, so they are limited in their contact with the water. Get more marginal plants - irises, pickerel, arum, forget me not, reeds, sedges, etc. - in your pond or some floaters and you'll find your water clearing up on it's own. If you're feeding your fish, stop. They'll be fine.
Is there any actual filter media on your pond? I'm guessing not, if you don't have a waterfall. Without biological filtration of any kind, green water is going to persist. Essentially nature is creating her OWN biological filter for your pond.