Whether or not you are responsible to pay the fee for the bloodwork that you in-network physician sent to an out-of-network laboratory would be best addressed upon review of your insurance policy for health care and consulting with your health care representative.What you have going in your favor for not having to pay for the lab work is that you did not direct the blood work to be sent to where it was sent. Rather, your in-network doctor did. I would also speak with your physician as to why the blood was sent to an out-of-network lab.