Lung efficiency with age?

The process that converts fat to energy releases CO2 and water as a waste product, that part is true. However, a decline in lung function is not a limiting process to this process; the two are independent of one another. Furthermore, it is not so much that the lungs lose elasticity, but more so the diaphragm, As a person ages, the  intercostal muscles become weak. This reduces the movement of the chest wall. Elasticity of the diaphragm, not necessarily of the lungs, is lost, and the diaphragm flattens, or tightens. The respiratory rate of well older adults slows, not increases, with age.

What do you think limits fat burning ability?

The way I see it is that older people move less because of stiff muscles and joints, which leads to a lack of mobility. Less mobility gives your body less reason to burn fat, which is technically a way to convert stored energy into usable energy.