Welcome to the site - at the same time, I'm sorry you're in the club. Stage IV lung cancer will definitely shake up your world. Nonetheless, I hope you find us helpful.
Depending on the location of the tumor, they may be able to actually do a surgery, but because your cancer is stage IV, it basically is in your blood (systemic) and able to crop up any place in your body. Removing a lung wouldn't stop the cancer or make a difference in your treatment and in fact, could weaken your stamina and resources.
What may be possible at some time is a VATS (Video Assisted Thoracic Surgery) that removes individual tumors. I had one to get a biopsy sample, but I think that it is also done for tumors that are causing breathing difficulty - although they can use radiation for that as well.
I hope that you have an oncology team that you trust. It can make a big difference.