No, you cannot save it. During the form filling process, you will only be given 60 minutes to finish it. If you exceeded it, any information you have already sent will automatically be discarded.
This is why early preparation(as early as now) is recommended so that during the application process you will be able to answer all the information needed in the form.
For more information on how to apply for the green card lottery, get your free copy of our Diversity Visa Green Card Lottery Book today.