Can I still be prescribed Vyvanse (lisdexamfetamine) over other add medications if I am changing to a new doctor?

Yes. Usually, a good doctor will take a complete medical history and review old records before continuing a medication like vyvanse (lisdexamfetamine). You can facilitate this by bringing in a copy of your medical records from your previous physician. If after reviewing the records and discussing your symptoms, the doctor feels like Vyvanse (lisdexamfetamine) isn't the best medication for you, they will counsel you appropriately.
Probably. What stimulant a doctor prescribes to treat adhd varies by many factors, among them the doctor's preference and your prior experience with stimulants. Another key factor is what stimulants your health insurance company covers, because that can affect your cost enormously.. If you are doing well, your new doctor will want you to continue to do so. But, he/she may still want to discuss options.