Does he eat organ meats, too? Some nutrients are better sourced from organs rather than muscle. You can look up what the nutritional content of meats and organs are and see what vitamins or minerals they're missing and what the effects of being low in those things are, as well as what timetable they kick in on.
Without carbs, he'll be forced to get his calories from fats, which is likely to be abundant in whatever meat he is eating. Lethargy, light-headedness, and nausea are very common in a person whose body is theoretically adapting to that difference source of energy. Anecdotally this could last from a day or two to a week or two. Your MC would be wise to scavenge for starchy roots or plants to alleviate some of these symptoms. Depending on how much hardship you want to throw at your character--some people experience uncontrollable diarrhea from sudden changes to a high-fat diet, rather than constipation.
Personally, I was on a stewed-meat-and-veggies diet for about one week a few years ago and felt very ill, to the point that I freaked out and got a pregnancy test (even though I was fairly confident I wasn't pregnant) because my symptoms were eerily similar to both of my horrible "morning" sickness experiences. I'm guessing it was a low blood sugar thing as I have a history of being on the hypoglycemic side of things. I also went down from about 128 lbs to 115, which I understand to be a terribly unhealthy amount to lose in the space of a week. Despite returning to my normal diet immediately, it took me about a year to gain that weight back.
Try googling "paleo diet" or "Whole30" or "ketogenic diets" as those are very protein-centric, low/no carb diets (that do include vegetables, ftr, so not quite a straight-across comparison, but similar). You might find some more stories detailing the symptoms of people who were/are on them.