Wrong. It's around the lung. The pleural space is the between the lung and the body wall, and it's most common to get fluid in there. You would not be able to siphon off the fluid that quickly or easily if it were in the lungs because of the separation by the alveolar walls and bronchioles *unless* the patient had the severest case of emphysema you'd ever seen.
Yeah, people need to think of what the condition pleurisy is when thinking of where the pleural space is. Friend of mine developed that after a bad bout of pneumonia. She said even childbirth wasn't as painful!