By "fat burning" you probably mean ketosis. It can vary, but generally speaking ketosis will end after you go up to 50 g of carbs.

If you don't have to lose weight, you probably don't need to be in ketosis, and could start at a higher level of your chosen plan. Or even just stop eating refined foods and sugar, etc.

You CAN still burn fat not being in ketosis. If you are taking in less calories than you are eating, you will burn at least some fat. Doing cardio on an empty stomach will also help burn more fat.

The advantage of ketosis for those of us trying to lose is that it reduces your appetite, and keeps insulin under control -- which means no cravings.

If you are considering LC, it's worthwhile to do some reading so you know how it actually works and the relationship between carbs and insulin.

There's lots of good info at the Atkins website, and the Atkins book or Protein Power are available in paperback for a few bucks, or from your local library.

Good luck.