Has he lost weight? Is he at a lower BMI than the other kids on his team? 133 at 5'11" seems really low, but for many endurance runners, a BMI at 18 is not a problem. Has his diet changed significantly since March? A nutritionist is going to look for nutrition problems, but might be missing out on something not nutrition related.
As for lifting weights and not eating enough protein - I take protein powder after most of my runs and notice a huge difference with how fast I'm able to recover versus before I started taking it. I can't remember if this is your son who takes protein powder, or is that is the other one? I'd imagine if he is lifting weights a lot, he is fatiguing his muscles, and that is going to affect his running. Increasing protein intake after muscle damage (either from weight lifting or from running) will help speed up recovery time. This can be from a whole food protein source like meat or eggs or protein rich plants foods like legumes or beans, no one "needs" to take protein powder for recovery. I take protein powder because it is hard for me to eat enough protein just in my diet - I eat fish and chicken, but I don't feel like I need to eat meat everyday.
But... if he is weight lifting heavy and running everyday, even with increased protein intake, there might not be enough recovery time and he's just in a cycle of fatigue from overdoing it. Usually, runners are told to do heavy weight training later in the day on the same day they do a hard workout run, and then the next day is a complete recovery day. No weights, and if there is a run, it is a very easy paced run on a recovery day. This allows the body time to rebuild those muscles, since both weight lifting and running hard will break down muscle tissue. Doing weight training on easy run days is actually setting the runner up for problems because both hard runs and lifting weights damages the muscles, and no day off means no recovery, and could easily set up an overtraining situation that is difficult to get out of.
I think seeing a nutritionist is a very good idea. If he is interested in improving his running, he can learn a lot about what a healthy diet should look like, and ways that he can improve, and sometimes kids listen better when it is coming from someone other than their parents.
Has you had his vitamin B-12 levels tested? Low B-12 can present other symptoms, but fatigue is one of the most common. Other than sources such as nutritional yeast, tempeh, seaweed/kelp, etc, B-12 comes from animal products. The best sources are meat, eggs and dairy and if he isn't eating enough of those, there's a good chance he's deficient. Also Vitamin D - even if he's running outside, his body may not be producing enough Vitamin D.
Has he had actual iron tests done? Most doctors will include Ferritin when they order an iron test, but often it has to be asked for. Also, has he had a CBC? That will help determine if he's anemic.
It's good that the nutritionist ordered the Vitamin D, but I do think B-12 deficiency is a possibility because of the way he eats. It won't really hurt to supplement with B-12, but won't help if he doesn't need it. It really should be tested first to make sure he needs it and/or that he gets the right type and dosage of supplement. Is there a way you can get the nutritionist to add B-12 to the list of blood work?
If you decide to supplement, it's best to get Methylcobalamin (type of B-12) because that's already the usable form. In addition, sublingual or liquid forms, often work best, unless the nutritionist recommends something else.
I was recently diagnosed with a couple of chronic sensory issues and although they aren't what your son suffers from, I get what you/he are going through. Plus I have that gag reflex when I try to eat certain things/textures, so I understand what your son goes through when it comes to eating.
Maintaining proper body mass has become a serious social problem. A review of literature concerning the relationships between body mass and health-related fitness revealed significantly fewer studies conducted on physically inactive people. The aim of the study was to determine the relationships between BMI values and the level of endurance-strength abilities in 19-23 year-old women. The research was conducted in 2012 on 204 first-year female students attending the University of Warmia & Mazury in Olsztyn, Poland. Basic anthropometric parameters (body mass and height) were measured and the level of endurance-strength abilities was assessed using the 3-minute Burpee test. The conducted research indicated that overweight and obesity negatively influence the level of endurance-strength abilities assessed by the 3-minute Burpee test. Statistical calculations revealed that when the value of BMI increases by 1%, the number of repetitions performed during the 3-minute Burpee test decreases by 0.93%. They also indicated the usefulness of the 3-minute Burpee test in determining the influence of BMI on young women’s endurance-strength abilities.