This post is an excellent case study is how a modern group can take ancient and unrelated symbols and claim them as their own in order to sell the fiction that they are much older than they really are and boost their clout.
It seems unlikely that a Babylonian fish god would go around with a lily blossom on his head.
http://www.ancientpages.com/2016/10/10/ancient-symbol-fleur-de-lis-its-meaning-and-history-explained/