Is there risk of flying with a partially collapsed lung?

YES. I agree with dr.Siegel. Air travel, skydiving, high altitude travel, scuba diving with an unresolved pneumothorax is dangerous. There are different specifics to each patient. It is important you discuss your pneumothorax with your thoracic surgeon and seek guidance and instructions for safe activities.
Yes, low pressure. Airline flights typically pressurize cabins to the equivalent of being 5000 feet high. The pressure in the cabin is lower than while on the ground. If the lung is partially collapsed and the air pressure is lower, it is possible to not get enough oxygen. Would be best to treat and correct the lung collapase and check oxygen levels prior to flying.