I think the body will burn carbohydrates as its first preference for fuels. If there's no simple carbs available (due to your dieting) and consequently eventually after glycogen stores are gone, muscle stores are used as fuel and you want to preserve the muscle mass you have then I think you'll have to increase your weight resistance workouts (to build that muscle back up) and take Branch Chain Amino Acids (BCAA) before your workout. They'll help stop muscle mass being burnt as fuel. Something like a banana and sugar free yoghurt might be an idea straight after your weight resistance workouts.
What are you trying to achieve by the diet ? Is it fat loss ? If so then you might find a balanced diet (0 refined sugars) with High Intensity Interval Training (HIIT) is more effective at burning fat as a fuel source and the improvements in fat metabolism continue for many hours afterwards. Don't underestimate good sleep too and dealing with stress as the stress hormone cortisol will encourage fat stores. I'd recommend HIIT and Weight Training in each session - try that for a few weeks and see if that achieves what you wanted in the diet.
Alternatively go through that diet till it achieves its aims then go back to a zero refined sugar, low GI carb, quality protein (oily fish for example) Kind of eating habit - (Omega 3 rich oils I think can only help too) till you're happy you're eating right. Then start on a muscle building program with a Gym instructor who's qualified to give you a program that will do that. Remember to build up the weight training loads slowly to avoid injury. I think you might want to keep eggs and proteins prominently in the diet around that time. I wouldn't rely on just a diet if it's fat loss you're after. Ideally I'd do the things I said in the first and second paragraph. I think how effective HIIT is, with ZERO downside will amaze you - your cardiovascular fitness and fat burning ability will shoot up quickly. Weight training on top will build good lean muscle and set up for a later Bulk and Cut regime if that's what you want…..Good luck!
