Morning hypertension is very common in those with high blood pressure.
It is a part of normal day/night variations of all physiological body functions.
Acctually, after waking the sympathetic system is activated, and body is releasing hormones that can give you energy in the morning, and also increase blood pressure.
To avoid the morning hypertension, it is essential to maintain blood concentration of a drug at the critical early morning period with the use of long acting agents.
Drugs with adrenergic alpha-blocking actions are usually selected to control the morning hypertension.
Hypotension is a side effect of the drug (lisinopril in combination with hydrochlorothiazide, a diuretic, leads to more symptomatic hypotension).

Contact your physician to reconsider the combination of drug you use and the drug regimen.