Is it possible to lose four pounds per week and still maintain a healthy lifestyle?

Yes. Yes, it depends on how you're doing it. If you're maintaining a healthy diet and exercising, then that may be just fine. Remember, though, it's generally easy to lose weight at first because a lot is water weight. It gets harder as time goes on. Also, be sure to get good nutrition & take appropriate rest so you don't damage your organs or strain muscles. And follow up with your doctor regularly.