I had a single Fire Eel for years, and it started out shy but quickly became a greedy and aggressive eater. What little I have read about the Aus Lungfish seems to indicate that they are slow and clumsy feeders. I would think that a Fire Eel would outcompete the lungfish and gradually stress and starve it.
Considering the rarity and cost of an AUL, I personally would not even consider risking a small one like that with any tankmates.