Hi Geoffrey 12, and Welcome to Talk Parrots.
If you post a couple of pictures of your budgies feet or claws and its beak we might have a better idea what you are describing. Fatty liver disease is usually found in overweight birds who are not physically active and who are usually on a steady diet of seeds.
If your avian vet thinks your bird has fatty liver disease he will suggest a strict new diet for your bird and tell you to make him more active physically getting him to fly around and play outside the cage.
Your avian may suggest to give your bird milk thistle and dandelion drops he will show you how to give this to your bird as you will have to administer the medication daily. It's not expensive but you must make sure to get the proper milk thistle drops that is only for birds, make sure not to get any drops that have alcohol in it as this can harm your bird.
If the vet thinks your bird has this illness ask him to show you how to trim your birds beak and toe nails so you can learn to do this yourself. I had a canary with this illness and I had to trim his beak every 12 days due to his illness so I know it can get expensive if you need to keep going back to the vets just to have your birds beak trimmed every couple of weeks. My canary didn't have any problem with his toe nails growing long it was just the beak that grew way too long too quickly.
Changing a birds diet can be difficult especially with an older bird, you may have to keep the bird in a separate cage from the other birds while you get him onto a new diet and try to get him to have more exercise.
I hope the avian finds there is nothing wrong with your budgie and maybe its just time for the older bird to have his nails and beak trimmed.
Keep us posted and let us know what happens. Good luck.