I would venture to say you’ll lose weight, but how much will be fat and how much will be muscle?
Here’s the problem, that is not something you can stick with. You have no protein, no carbs . . there is a reason these are part of the "Daily Recommended" your body needs them.
You don’t say how old you are . . a teen still growing? How much weight do you want to lose?
I’d recommend you do it a bit different. You want to get your metabolism moving, not put your body in to a starvation where you feel awful and you’re not losing the weight like you should.
Breakfast - a piece of fruit is not enough. If you don’t want food first thing, buy a quality meal replacement shake. Otherwise, how about a couple eggs (you can hard boil and keep ready in the fridge) add a piece of wheat toast.
Snack - I have a small bagel and a handful of raw almonds. Or a couple eggs, fruit, veggies
Lunch - Sandwich on wheat bread. Turkey, Chicken, Tuna . . . add veggies. Chicken salads are great.
Snack - See above
Dinner - go for wheat pasta, wheat bread, brown rice over white. Chicken, turkey, turkey burger.
Add quality supplements. If nothing else a good multivitamin. Add water, remove sodas, mocha’s, lattes.
Add exercise.
I know it sounds like you’re eating all the time and you are. But you’re making healthy choices and you’re not walking around hungry. Your energy will increase and you will go down in sizes. I’ve gone down two sizes since changing my lifestyle and clients that have done the same. It works. You need to put something nutritional in your body every 2 -3 hours .. never more than 4.
The big part is staying committed. Make the decision and act on it, but do it in a healthy way.