Indeed what he described sounds a lot like low/no-carb diet, also known as ketogenic diet. While lots of people have success on it, it isn't a panacea: the closer you get to "normal" BMI, the more you will have to manage caloric intake, and for a minority who attempt it, ketogenic doesn't work for them at all. Lots of caveats, but one I see increasingly as more people pick up ketogenic dieting: many go overboard on the protein part, which metabolizes into carbohydrates and defeats the intent. Very, very roughly about 80% of your caloric intake will be comprised of fats, 15% protein, 5% carbs (if any appreciable amount; some will restrict down to 20g or less per day). Go slow, modify one variable at a time, focus on long-term (3+ year) consistent weight loss, accept your lapses with grace, and good luck.

It sounds like a keto diet, which I adopted about a year ago and have lost about 50 pounds on (from ~185 to ~135). I learned about it most from /r/keto on reddit.

Bacon and eggs diet sounds very much like keto. If you don't have already critically high blood pressure and your kidneys aren't damaged for some reason, do try it out.

I'd recommend you read Reddit's /r/keto, specially its side bar, and make sure you always meet water intake goals and take your electrolytes.

I've consistently lost weight on the diet, and consistently gained it back when I abandoned it because Doritos.

Just eat bacon and eggs if you want but make sure you count how many calories you eat during the day and keep it below your TDEE.

Most likely ketogenic diet. Check out the /keto subreddit FAQ.