If your body is struggling to recover and build from one strength session to the next then add in protein. If you're struggling for energy then you need to eat more to replenish. However it's very hard to workout every day, maximise performance and yet still lose weight. If it were me I'd go keto so you can use your bodyfat stores in recovery without suffering the next day. And to play it safe you can go cyclic, you don't want to have the same deficit every day. I'm not sure that lunch in your plan is really doing anything much. I'd probably consider occasionally skipping breakfast too, and concentrating on dinner. But then sometimes you could miss dinner instead. Eat the right foods and this can come naturally, losing weight while maintaining energy and performance. Hard to keep up the intensity for too long without a break though, whatever you eat.

Obviously Leangains is almost certainly the best resource for what you're trying to achieve.

Unless you're keto-trained, your body is going to prefer glycogen to fat as the primary fuel during the workout, so while you could rely on bodyfat for the energy, it won't be ideal.

Immediately post-exercise is when the muscles are most receptive to replenishing, so milk or another glycogen replenisher is a good idea, especially if you're working out twice a day. Weight loss is based on overall calorie deficit, and exact timing has little bearing on that. As long as you are eating below maintenance (but not too far below or you risk sacrificing performance) you will lose weight.