Like most diets for people everyone has their own ideas. Your cyclura won't die without animal protein. With a good veggie diet and proper cyclura husbandry they will do just fine. Too much animal protein can cause kidney and liver damage. They're designed to eat plants and that is the majority of the wild diet but they do eat animal matter in the wild too. No one knows how much that is though. A little or a lot of protein, better safe than sorry, or somewhere in between, thats up to the owner. You will find both ends of the spectrum on this list.
I give mine less than 5% of their diet. Generally, the thought is- the more animal protein the bigger they get faster but you risk shortening the life span. Read all you can and ask questions then its up to you.