To explain the question: if I, a fat person, go on a diet/exercise regimen and lose fifty pounds, how much of that mass exited my body through the lungs?
Do you mean by evaporative water loss?
Both water and carbon.
For all practical purposes, all of it. The fat lost consists of carbon and hydrogen. The carbon itself will be lost as cabron dioxide through the lungs.
The hydrogen is lost as water. Camels and other desert animals can actually gain metabolic water from metabolising fat, but humans can’t. The extra oxygen needed when the fat is metabolised increases respiration so much that we actually lose more water in our breath than the water gained. So once again the fat is going to be lost in the breath. Note that this doen’t men that exact same hydrogen atoms that made up the fat are lost in the breath. Most of them will in fact end up in the general body tissues, but the net mass loss will be the result of other hydrogen atoms lost in the breath.
There will also be an immeasurable amount of connective tissue lost, and the protein from that will be excreted in part through the urine, but all the fat itself is lost as water and carbon dioxide from the lungs.
So for all pratcial puproses all the weight you lose is lost through the lungs, either as water avpour or as carbon dioxide.
About what percentage of what you ingest is lost as energy that is used for living?
The amount would be immeasurably small. WAG would be less than a gram over a lifetime.