If you owe a medical provider or if your insurance company has paid your emdical expenses, the medical provider or the insurance company can serve your lawyer with a lien. He really does not have a choice - if he recovers for you and does not pay the liens, he can be liable for the amount of the lien.
The fact that there is a lien does not mean that you do not still owe the money to your doctor. Many doctors will wait for your recovery but they do not have to do so.
It is always the patient's choice how to pay for the medical services. If you agreed to pay your doctors with a lien on your recovery, it is your right to do so. If no one notified the new lawyer about the liens before the settlement was distributed, you are directly liable to pay the medical bills yourself.