Cars are very susceptable to EMP... as are all home electronics.

Lead shielding would protect against certain types of radiation, but
isn't needed for EMP protection.

If you are really concerned about it you can make your own Faraday
cage for your car inside a garage... basically, make a 2x4 open frame
that surrounds your car and cover it with metal screening... like
copper or galvanized steel screen.  All the sheets of metal screen
have to be very well electrical bonded approximately every 3" or so
(spot solder) along the seams.  You could also buy one of the
all-metal vehicle storage sheds and store it in that, again making
sure there are no gaps and all individual pieces of metal are well
bonded together.

The hardest part to close gaps and ensure it's bonded  will be the
door.

The cage doesn't have to be grounded to work as a Farady cage, but it
is recommended in case it should come in contact with line voltage
(like a frayed extension cord).  It would be better to blow the
fuse/circuit breaker than create a giant piece of uninsulated metal at
115v AC!

You can also buy rolls of plastic sheeting that has a metal film vapor
deposited on it.  Your can then heat-seal the sheets together to form
a giant airtight bag around the car.  Throw a couple pounds of
dessicant in there, suck out the air and back fill it with nitrogen
and you can preserve the car for a pretty long time too!

Survivalists have already thought this one through... check out some
of their web sites and you'll get much better ideas than mine.