Hi Jackie, the short answer is yes. A lower is a lower. It is not a pistol or a rifle until you attach the upper.
There are other factors too. You may need to change the buffer tube, buffer weight, or buffer spring. Too much to detail here, you would need to google & do some research.
With that being said, you cannot legally put a pistol length upper on a gun that was registered as a rifle. You cannot convert a rifle to a pistol.
If you have a virgin lower that is registered as 'receiver', then you can make it a pistol, then a rifle, and back to a pistol again.
If it is first registered as a rifle, it can only be a rifle.
Stay safe & have a great day!