I'll second the input from either a Certified Avian Vet or Avian Specialist Vet FIRST, BEFORE giving your bird anything at all, as it depends on what is actually causing the Liver issues to whether or not Lactulose, Milk Thistle, or anything else will help or hinder your bird's issues...Also, if your bird has Kidney issues in addition to the Liver issues, as they often do, then things get a bit more complicated, because certain things that can make the Liver better will make the Kidneys worse and vice-versa...And that's the same reason that feeding them a high level of protein is not good in this situation, because it will tend to cause secondary Kidney issues, such as visceral Gout, as it causes them to not be able to rid their bodies of Uric Acid and Creatinine...
***How do you know your Cockatoo has Fatty Liver DIsease? I'm going to assume that you already have a CAV or Avian Specialist Vet and you've already had complete Blood-Work and X-Rays if you know that your bird has Fatty Liver Disease...If not and you're just guessing or assuming that he does due to a previously poor, high fat diet, then that's not at all necessarily true, so you don't want to ever give anything at all, prescription or holistic supplement, until you know for sure what your bird's Liver and Kidney values actually are, and what the underlying cause of any issues in his levels are being caused by...
That being said, specifically for treating Fatty Liver Disease and other Liver tissue damage, Milk Thistle is one of the most effective herbal/holistic treatments in the world. It's WIDELY USED to treat Fatty Liver Disease in bird/parrots, reptile/amphibians, dogs, cats, rodents, and humans, and it works better than any prescription Liver medications I'm aware of...But as already mentioned by Noodles, it is boosted by the use of Lactulose depending on what the underlying cause of the Liver Disease is, and whether or not there is also Kidney Disease as well, and the only way to know that is by complete Blood-Work, Fecal Cultures and Microscopy, and an X-Ray. You don't want to just start giving your bird Milk Thistle if you haven't already done all this with a CAV or Avian Specialist Vet who has much education and experience in treating Liver/Kidney Disease in Parrots, they've done all of this appropriate testing, gotten the results, and you've developed a treatment plan AS WELL AS A SPECIALIZED DIET together with the CAV...