Congratulations on an efficient fat-burning metabolism! How long did it take you to get there?
Fat is extremely satiating, all the moreso if you're not used to eating it in large amounts. A common trick is to eat your protein first, then top up with fat.
The human body is designed to weather periods of protein shortage, so it's not a big deal if you go without for a while. Just keep an eye on your lifts and your running time to make sure your performance isn't cratering.