How do you educate a patient who feels they do not need to take their medication and can solve their medical issues with improved diet and exercise alone?

Diet and exercise are completely passed over in the medical field, especially by those prescribing, so most of them are not willing to accept the idea that patients can get better with JUST those improvements. If your patient is unwilling to take meds, encourage them (or the doc) to have lab work done beforehand and then give them a short period of time (depending on diagnosis) to eat better and exercise more, but lay out clear expectations. After this period, have them do more labs to compare where they were beforehand. Some patients may improve dramatically with improved diet and exercise alone, but those that don't can now see evidential proof that it's not enough. Let them be the ones to decide it's a good thing, because coercion never feels good.