There is no evidence that drinking lemon with hot water or consuming coconut oil can cure cancer.
However, this advice is dangerous. There is no evidence that these dietary habits will kill cancer cells. Experts have warned that alternative treatments can cause other side effects and cautioned against using unproven "natural" remedies for any disease.
According to Cancer Research U.K, there is no evidence a sugar-free diet lowers cancer risk. All healthy cells need glucose. Reducing sugar intake can starve the body's healthy cells of necessary sugars. Restrictive unproven diets can also hinder the patient's recovery from the advised treatment. It said, "There’s also no evidence that adopting a diet very low in carbohydrates will lower your cancer risk or help as a treatment."
Drinking lemon juice for several months will also not cure or make cancer disappear. As the University of Arkansas for Medical Sciences (UAMS) says, "there is no proven scientific replacement for radiation therapy or chemotherapy."
Michelle Morgan, a clinical dietician, advises patients to follow the recommendations from their cancer treatment team and not to believe the "anti-cancer" food claims circulating online.
There is also no proven evidence that organic coconut oil can cure cancer. An NCBI study did find that a few components of coconut oil can affect some forms of cancer, finding that the lauric acid found in coconut oil can hinder the growth of cancer cells, leading to their destruction. However, the study also said more experimental evidence is required to define better action of the lauric acid for cancer.
In short, there is no evidence that these dietary ways can cure cancer or kill cancer cells. Following alternative therapies could prevent conventional treatment from working effectively.