The reason for the cough is something to pay close attention to.

The agent is bradykinin, which builds up in some people because they are low in the enzyme that degrades it.

The cough can be a serious warning sign of angioedema. It can swell your throat until you cannot breathe at all.

I had this happen to me this winter...I swelled up all over and had terrible pain. So please contact your doctor and get that drug changed and never take it again!

Acquired angioedema is a real, life threatening situation:
http://www.hcplive.com/publications/...-04/2005-04_02

You may or MAY NOT have hives with this. Mine did not have hives at all. I took ACE inhibitors for about a decade, but the lisinopril was the last straw. Evidently, my metabolism could not handle it (previously on Vasotec) and I had a very painful crisis.
You can die from this if your throat swells up enough. So you must report your severe cough now, and get off all ACE inhibitors.

http://www.haea.org/about/
Doctors are now getting Continuing Education on this subject, as up til now it has been hidden and not recognized. People inherit the inability to remove bradykinin from the body, in various degrees, and the special blood tests on the HAEA website explains them, and how to interpret them. It is best to find a specialist called an immunologist for this evaluation.

One thing doctors do not often understand about Lisinopril.. This drug is excreted whole (unmetabolized) in the urine...and for me at least this caused terrible bladder pain when I had my reaction.
This can simulate a bladder infection, but it is not. If you have this bladder symptom, it is just another reason to get your doctor to give you another blood pressure treatment. NO MORE ACE inhibitors!