Can low blood pressure cause you to feel dizzy with eyes closed when lying down and fine every time else, like bending head side or down. ?

Probably not: If low blood pressure is source of sensation you are calling dizziness, it would usually worse when you are upright. There are certain types of vertigo and disequilibrium that are worse when you have your eyes closed. Consider an evaluation with your pcp about whether your blood pressure is low or other causes for these symptoms.