Dr. Jason Fung has done extensive research and experiments on this topic including fasting. You can read his research in his book obesity code. Very eye opening.
I'm sure it could also yield multiple well-cited articles on the other side as well. It would be much more helpful to actually provide some research that you stand behind.
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.