I would agree with other posts here. The ace-inhibitor worked for you with a side-effect of cough so switch over to an ace-blocker(angiotensin II antagonists are the appropriate name). Basically same overall effects without the cough as a side effect (cough side effect comes from a chemical known as bradykinin). Where the ace-inhibitor blocks the action of an enzyme in a pathway, an ace-inhibitor blocks it's action at the site of binding. Bottom line: no effect on bradykinin, no effect on cough. As mentioned above: Atacand , Cozaar, Diovan , Avapro, Micardis
Others have mentioned HCTZ as being first line therapy. This is true and i would typically recommend a switch to that however, you have past successful experience with an ace-i (lisinopril) so i would change my recommendation to stay within a similar class.
Look up RAAS (Renin Angiotensin-aldosterone system). If you look for a diagram of the pathways, you can see where ACE-I's work. They block the conversion of Angiotensin I to Angiotensin II.