Can fluid build up from latissimus dorsi clap cause fluid to also build around lung?

The fluid buildup around the lung is likely due to surgery, but not specifically the latissimus flap. General anesthesia, specficially with a breathing tube, coupled with immobility can lead to pleural effusions. Having surgery on that side of the body, coupled with this, can lead to a unilateral pleural effusion. Typically this will resolve on its own although admittedly it can take a while. I would make sure that you are following up with your primary care physician along with your plastic surgeon to be sure that his resolves in a timely fashion.

A seroma may develop after latissimus dorsi breast reconstruction. A seroma is a pocket of clear serous fluid that sometimes develops in the body after surgery. This fluid is composed of blood plasma that has seeped out of ruptured small blood vessels and inflammatory fluid produced by the injured and dying cells. This will usually develop between the ribs and the skin, not the lung.
A pleural effusion is a buildup of fluid in the pleural space, an area between the layers of tissue that line the lungs and the ribs. Many things can cause a pleural effusion including but not limited to fluid status, infection, pulmonary emboli and hydrothorax.

At 5 weeks there is still inflammation around the site of surgery that may cause fluid. But not necessarily because of the implant. I would recommend to follow up with your plastic surgeon about this fluid. 

No, not unless there is an infection under the flap. Usually, edema fluid or seroma builds up and is removed either with a drain or needle. The pockets do not communicate with the lung. If there is an infection or the patient is not deep breathing due to pain, fluid can build up in the lung. It is important to walk, deep breath and follow all instructions to prevent complications.