It would depend HUGELY on the atmosphere of your world.
But assuming Earth sealevel normal:
Simple damp skin, well-supplied with blood circulation, is enough to survive and will work in air or submerged. It would only support very minimal exertion though.
This is exactly what a normal lung is, just with a very convoluted geometry to fit more surface area into the same volume, and to keep it moist.
It is also what gills are, except that gills tend to be optimized for use in water.
Both lungs and gills are merely damp thin skin exposed to the environment, with structures to make as much surface area as practical.
If your creature needs a constantly active lifestyle, it will need lungs or gills.
If it only requires a burst of activity interspersed with long periods of inactivity, consider storing oxygen in internal storage organs.
Wild idea: creature has bare-survival-level lungs/gills/whatever. It also has oxygen storage ability. The Nest is a construct or symbiote that is sessile, and gathers a store of the oxygenated juice. Effectively, you could have a mobile creature without the encumbrance of complex lungs, but capable of high metabolism by ingesting both fuel and oxygen from external sources.
A creature with a build-in oxygen reserve like this would be a very scary thing in a fire. Containing both fuel and oxidizer, it would be somewhere between flammable and downright explosive!