How does lemon and water help in reducing weight in an obese person? What is the mechanism of action?

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My two cents. It depends how the lemon and warm water is applied. If the only thing that the persons eats is just lemon and water the person will lose weight because of the decrease in the calories, but it is impossible to survive on it. In my 20 years of experience I see that people try to take short cuts and they want the magic pill or the tea that will help them lose weight instead of making permanent lifestyle changes. I searched the literature and I could not find any reputable clinical trials on lemon and warm water. What the person needs is to identify the origin of the problem (endocrine? depression? low-self worth? too much calories?, etc), that is our approach to the problem of depression: https://www.researchgate.net/publication/278411982_Nedley_Depression_Hit_Hypothesis_Identifying_Depression_and_Its_Causes and we are showing a 95% response rate. One last thing, if you noticed many of the weight lose clinical trials will show that the placebo group actually lost some weight. Placebo has a powerful effect, if you truly believe it will make you lose weight you probably will.

PS I see that you are in Rajasthan I was there a few months ago I went to Jaipur and Jaisalmer and did some lectures in CMC near Chennai...

The lemon and water theory of losing weight has been on the public domain and some have even given testimony of how after drinking the lemon and water "detoxification water" have lost upto 2 Kg within two weeks.  There are several recipes on detox water which are made up from different fruits and herb for example https://54health.com/food-and-drinks/detox-water/.  Most of the recipes contain lemon as one of the ingredients or cucumber so there should be something in these products which is believed to be the main ingredient and/ factor of weight loss.

Some of the instructions of taking detox water are that the person drinks upto 4 glasses per day front-loaded from first thing they take just after waking up in the morning to midday and then pure water for the rest of the day (these glasses are supposed to make up part of the fluid intake requirement of the day) for two weeks and then after two weeks they are supposed to be taking it through out the day as part of their diet menu until they are used to it to be part of their lifestyle of taking up to 4 glasses of detox water per day. 

The detox water is supposed to:

The citrus fruits and other fruits and vegetables are also commonly listed as foods that boost you metabolism in addition to most green leafy vegetables, herbs, spices and high protein foods. 

Please take a look at this useful link.