Basically, you can certainly go into starvation mode, but not in any reasonable amount of time. Skipping meals or even fasting for a whole day will not cause "starvation mode". Prolonged calorie restriction can affect hormones like Leptin and affect energy expenditure.
Bear in mind that Lyle believed in "starvation mode" 10-17 years ago; I believe he mentions it in his first book. He was also a firm believer in strict caloric arithmetic and that microbiome didn't matter. His content is only as good as the current scientific literature is, and that has changed a lot in the past 20 years.