Almost sure you can lend your car to family (or anyone else) if they have a valid driving licence which is recognised in Greece. Unless things have changed recently, it's the car that is insured, not the driver (although the recent move by an insurance company not to reinsure a customer over the age of 70 when they changed the car, rather casts that in some doubt). Ask your insurance agent, to be certain. Bob.
Yesterday today was tomorrow. Don't dilly dally!