A pond of that size equates to about 1800 gallons brimfull. You would need at a minimum a pump/bio filter system capable of turning over that quantity of water per hour in the summer. Aim for a pump of 2000 gallons per hour to cover pump losses due to bends/joins in the pipe. Additionally you would need a uv light of a minimum of 20watt.
Fish produce nitrite in their waste products, the more you feed the more nitrite produced, do not overfeed them, (in fact keep them mean and lean!). Nitrite is converted in the water by bacteria to Nitrates. Nitrate is used by plantlife for growth. Growing Marginal/Submerged plants uses the nitrates up. Insufficient plantlife means excess nitrates left in the pond. Green water is just Algae in suspension. Algae needs water, sun and nitrates to grow and multiply. Algae can be killed by UV light.
All ponds are overstocked with fish in terms of size, number and type. It wouldn't be much fun with only one or two fish in 1800 gallon pond! My pond has more fish than yours but is smaller. You have to artificially assist Mother Nature to balance the pond.
Before you do anything else consider buying a water test kit from an Aquarium shop and test the water to see what the levels are, you should be aiming for an almost neutral reading. The kits are not very expensive.
Your lilies are almost certainly being eaten by your Koi. I've given up trying to grow Lilies my Koi somewhat bigger than yours take great delight in eating the leaves as they start to grow.
Encourage some floating plants, because they will add shade and use nitrates. Do not buy 'Fairy Moss' though because this is highly invasive and grows like 'billy ho', nightmare to remove and eradicate. It would swamp a pond within a few weeks and would take about 2-3 yrs to eradicate, I know this from bitter experience!!!
Best of luck ☺