When a car is repo'd can the lender tell you the only way to get it back is by refinancing?

NO they can tell you to pay the back payments and fees (for the impound) YES. At this point it is pretty much whatever the lender wants and they usually want ALL of their money NOW. Are they suggesting that you refinance with them or go elsewhere for a new loan? If you didn't make the payments on the old loan, it is unlikely that they want to give you another and you will have a hard time finding another lender who will give you a loan when you write "pay off repossession" as the proposed use of the funds.