The lungfish is native to Africa and has gills as well as a primitive lung that allows it to breathe on land for short periods of time while it searches for water.
When the dry season arrives and the rivers dry up the lungfish will cocoon itself in a mixture of mud and mucus under the ground and hibernate until the water levels rise.
When the lungfish is in the water, it has to swim up to the surface for oxygen every half hour for a gulp of air to avoid drowning.
Although they only have gills crabs are able to easily transfer between the land and sea. This is because they are able to breathe through the moisture on their gills, using the process of osmosis*. As long as their gills are moist some species of crab can survive on land for large lengths of time.
Can retain up to 20 gallons of water in their bloodstream and therefore can go without water for a considerable length of time.
Conclusion: Designing how the creatures of Pan breathe
Due to the Planet Pan having 12 moons, the weather patterns and sea levels are changeable and sporadic. Therefore the creatures and people need to have evolved gills as well as lungs in order to survive.
Their gills will be similar to that of a crab in that, if they keep their bodies moist then they can survive out of the water for extended periods of time. The average creature can be out of the water for about 2 months without drying out. In order to keep their gills moist they can excrete water retained in their bloodstream onto them, this is similar to how a camel stores water. However, due to constantly using water to moisten their gills, they have to replenish water supplies regularly.
They will have a primitive lung, similar to that of a lungfish, allowing them to breathe for a short amount of time until they reach water and hydrate their gills. Also, similar to the lungfish, if there happens to be a dry spell, which occasionally happens, they can make a type of cocoon to nest in until the water levels rise, or to protect themselves from the chaotic storms that can occur on Pan due to its moons aligning.