What drug would be a good replacement for lisinopril?

Olmesartan is the best choice when the pt start with cough by Lisinopril.

The medications mentioned by Stephen Treloar are all different brand names for Lisinopril. Why do you plan on switching the medication? if you are looking for a medication of the same class (ACE inhibitors) that you can tolerate better then you can consider (Benazepril, Captopril, Enalapril or Ramipril). If you had really bad side effects and want to switch to a medication of a different class that the possibilities will be endless and your doctor would have to decide what class to switch to based on your side effects.
Classes of Anti-Hypertensive medications include: ACE inhibitors, Beta Blockers, Calcium Channel blockers, Diuretics and a few others.

This is probably best answered by your doctor who knows your medical history and details. That being said, drugs.com lists 3 related drugs and support groups:
"Related Drug Support Groups
Zestril, Prinivil, Qbrelis"