Your systolic (top #) readings of 120 are great.
120/70 is a textbook normal and desirable blood pressure reading.
The diastolic (bottom #) reading of 50 is a little low but if it is temporary and not sustained, it shouldn't be cause for alarm.
Yes, BP lying down is usually lower than when standing.
I notice from other posts you've made on other boards that you're trying Dyazide (fixed combo drug of HCTZ and Triamterene, both are diuretics) for a vestibular disorder.
If it drops your BP too low, it could make you feel more lightheaded.
Store machines are usually not reliable (although you might get lucky and find one). If you need to track your own BP on a regular basis, it's best to buy your own home monitor. The new ones are digital, fully automatic-inflatable and very accurate.
If you continue on Triametrene (potassium-sparing diuretic), your doc should take a blood test to make sure your potassium levels aren't climbing.
zuzu xx
P.S. If the Triametrene is helping you with your vestibular disorder and you feel better on it, I would not worry about the BP readings. Low BP is something most people would be happy to have. It only becomes an issue if it causes symptoms.