Is no carb diet, to lose weight, healthy in the long run?

Not no: No. Low carb is healthy. No carbs are not in any way healthy.

Type of carbs: They should be low glycemic index This means they don't increase blood sugar which then increases insulin with result of increasing inflammation So it's the type of carbs that matter. There are good and bad carbs, good and bad fats and good and bad proteins. Inflammation is the cause of most illnesses (cancer, heart disease, dementia etc.)

No: your body needs carbohydrates for metabolism to run efficiently. Without carbs in your diet, your body is breaking down protein and fat to run your body. It not healthy. Your body is also making wastes ketone bodies that have to be excreted in the urine to prevent your body from excess ketones, its another unhealthy state.