LBM and Fat loss

Ladiez and Gentz, Pimpz and Playaz
It was mentioned that an increase in LBM would effectively burn more fat…yes indeed, i am aware of this, but when dieting, what is the specific physiological mechanism that should accelerate fat loss…say i am 195 with 9% body fat, and start a keto…once in a catabolic state, does the muscle continue to burn stored fat (i.e., oxidizes it to stay alive?) or does it burn calories in teh body first, which then once depleted, the nervouse system oxidizes fat to fuel itself…if the muscle tissue doesn’t get the required daily calories it needs for sustenance, does it simply die off?..i too have noticed that each time i diet back down, it seems to become a bit easier to get back down into the 5-7%body fat range coming from 9ish percent…any technical explanations here are very welcome.