This is a great writeup and Lane's book looks pretty interesting. One thing I'd add is that knowledge of the Krebs cycle (aka, 'tricarboxylic acid cycle') helps people understand why some dieting approaches seem a bit unwise to biochemists. A simple explanation of the Krebs cycle is that it is a kind of engine that sits at the center of metabolism, but metabolism is not just the breakdown of molecules for energy, it's also the construction of molecules for various cellular needs. Take this quote as a beginning point:

> "...we were told the monstrous names of its component parts—succinate, pyruvate, Acetyl-CoA, cytochrome c—while, on the blackboard, we counted NAD+s and FADH2s, and followed “redox” reactions as they “oxidized” or “reduced” elements."

From a biochemist's point of view, there are about three classes of foodstuffs - carbohydrates (which break down to simple sugars), proteins (which break down to amino acids), and fats and oils (which break down to fatty acds). All those breakdown products are fed in one way or the other into the Krebs cycle (for amino acids, the nitrogen is stripped off and excreted as urea). These energy-producing (i.e. NADH / ATP generating) reactions are grouped under the heading of catabolism. If you entirely exclude any of these three classes of foods, such as by ingesting only protein, the Krebs cycle and affiliated metabolism starts doing some funny stuff. This is the basis of 'eat a balanced diet' advice.

Note that the Krebs cycle also sits at the center of your body's biosynthetic system, which is continually manufacturing the non-essential amino acids, as well as sugar and lipid synthesis, which then form the basis of hormone and neurotransmitter synthesis. The molecules in the above quote are, in various cells, exported out of the Krebs cycle and into these biosynthetic pathways. Unbalancing the Krebs cycle by depriving it of essential feedstocks can thus throw a lot of your body's fundamental systems out of whack. Since the Krebs cycle is highly regulated and somewhat malleable, it can respond in various ways to account for this, but problems can arise over time.

Hence, the best dieting approach for losing (adipose, i.e. fatty tissue) weight is most likely intermittent fasting with a carefully balanced (carbs/proteins/fats) diet, just less food overall. Under such fasting conditions, the fatty tissues get converted to things like ketone bodies and hence to glucose (the brain's primary fuel). Here's a collection of abstracts on how this works in intermittent fasting (it's also related to diabetic issues):

https://www.sciencedirect.com/topics/agricultural-and-biolog...

Note that regular exercise is also good for your health, but that's not necessarily 'burning fat' so much as it is improving your circulatory system, and flushing your lungs with plenty of air, as well as improving muscle tone.