If you can find out the cause of the low blood pressure then you treat the cause. Say a person has anaemia by treating the anaemia it should solve the low blood pressure.
Hi Jam my bp is very erratic. It can go high 225/90, I'm on bp meds or low 90/60. When it goes low I feel dizzy as you stated. I drink 3 ozs of water with about 1/2 tsp of salt in it. It raises bp very quickly. It's a quick fix, not a cure.
One of my friends used to have low blood pressure in the morning especially when he stood up after awakening. He was prescribed some medication for it. I think your Doc may not be considering such a medication at this stage and keeping in view your situation.. He may prescribe some medication when so inevitable.