No, broadly, you should not be worried about eating too little if you are not hungry. Part of the reason LC works so well is that it reduces appetite and you are satisfied with less hunger. Part of how that works is that insulin levels are reduced so that your body can access stored body fat for fuel, instead of needing to eat regularly.

HOWEVER, it sounds like you are concerned about past disordered eating and you are afraid of slipping into it again. That should give you concern. Recognizing a problem is the first step in solving it. Recognizing a potential problem is even better.

Perhaps (because of your personal history) you need to take a more moderate approach. Lay out on paper what you are going to eat every day - make sure you are getting whatever level of carbs you set for yourself (20 g, 50 g, whatever) and a minimum but sufficient amount of protein (60-80 grams per day is a good level for most women). Eat that minimum amount of food along with enough fat to keep you satiated (listen to your body). I would not shoot for any particular level of fat or any special % of macros because once you are fully fat adapted, your body can draw from your fat reserves to give itself all the fuel you need (until you reach goal).

Just concentrate on getting some protein each day and enough LC vegetables to give you vitamins and minerals, electrolytes. Make sure you are getting enough salt. Then let your body tell you how much fat to eat.

All the best to you. It's a very good sign that you recognize the potential for disordered eating and are trying to address it from the start.