Why my results have time delay when I use LSTM?
I've had similar results when working with time series data. My conclusion was that the model does not learn any real pattern, except that the next value is pretty close to the previous one (or a smoothing of previous ones) + some noise. 

This can be easily verified, if you feed your model's predictions recursively into the model to further predict the future (multi-step ahead forecasting based on the model's predictions). In the above mentioned case, your predictions will explode exponentially pretty quickly.