Can lack of sleep increase b.P?

YES. and so do Sleep apnea/ Stress/ anxiety/ coffee/ smoking/ being overweight and sedentary lifestyle as well as a diet high in sodium intake.
Yes. Restful sleep is important for healthy body. Lack of sleep causes many problems such as high bp. For eg people with sleep apnea wake up frequently at night, get little oxygen to the brain and BP is high during day.