13 year old dog - left eye - 3rd eye lid half way up - both top and bottom lids droopy. Pretty sure he hasn't had a stroke. I know that there is something called h--------- syndrome?

Had a dog 15 years ago that had the same symptoms, you don't usually have to treat it, its a bit like a paralysis in the face.

Any ideas?

Hi Yappy

Are you thinking the problem is called "Horners Syndrome" ?  If so I had a young male puppy aged 5 weeks old that started to show signs of it a few years ago.  No treatment was needed, just fake tears to help lubricate the eye ball, and time was the healer.  At just a mere 11 weeks old this little fellows eye was back to normal and now four years old and has never shown any further signs of it happening again.
He was seen by the vet every two weeks to keep an eye (pardon the pun) on it, but was informed only time would help heal the nerve damage. And it sure did the trick with him :-)

Here are a few websites that helped me.
http://petcaretips.net/horners_syndrome.html
http://www.thepetprofessor.com/cat-info/horners-syndrome.html
http://www.eyevet.ca/horner.html
http://www.vetinfo4cats.com/chorners.html
http://www.gvsvet.com/horners.htm

Hope this helps