This plan WILL work for you, particularly considering you are so young. I would not generally recommend a 40 day fast without professional supervision, as many changes can call for professional assistance (like the kidney crisis I had on day 18 of my 60 day, supervised fast). Also, there can be many metabolic changes with weird side effects like hair loss (I lost hair by the handsful a month after that 60 day epic, and thank goodness my excellent naturopath was able to explain the changes taking place, and that the hair loss would stop--it did)...
30 days is a safer goal, but monitor your progress every ten days. See how you are feeling and make the decision to break or continue at that time.
An alternative to a long fast is to fast ten days, eat a cleansing diet for ten days, fast another ten... I did a series of five last summer and it was much easier on the body than a long haul.
Presuming you are pretty clean (though nothing stores toxins like fat), you should do well. Remember to keep your colon VERY clean every fasting day, and drink lots of water in addition to the lemonade. DO exercise daily, unless you are in a crisis, and you will increase your detoxification and lose weight quicker.
Have a wonderful cleanse, and best of luck with your plans.