Lisinopril reduces your blood pressure by lessening the diameter of the blood vessels in your body. It is classified as an ACE inhibitor (angiotensin converting enzyme.) Think of it as if your finger is covering part of the end of a garden hose. The water goes farther out because the volume remains constant, but the diameter at discharge is less. Hence, higher pressure. Reducing the diameter reduces the pressure. Lisinopril, and any other “ -pril” medication works like this.
Lisinopril is well known to create the (in)famous lisinopril cough. Some are definitely worse than others.
If this is the case here, your doctor may write for a beta blocker. This family ends in - lol, such as atenolol. These meds work to slightly slow the heart rate. They are completely safe. Think less blood volume, therefore less pressure. I have been on a beta blocker for several years. Always be proactive in addressing any med reaction with your physician and demand a change if any untoward side effects are felt.
Sorry for the lengthy post that is slightly off subject. But... Knowledge is power.
I took 20 mg for years and then I retired and my blood pressure dropped dramatically. I no longer take any bp meds.