The AE-L/AF-L can be assigned different behaviours - therefore you will need to identify first what behaviour it has been given.
In order to check, enter the camera's menu, then Tools and finally the Buttons settings.
I think that the D3200 proposes 5 behaviours, all linked to auto-exposure, auto-focus or a combination of the two.
The default behaviour should be that it locks the two, exposure and focussing, together.
Supposing it is on the default value (both auto exposure and auto focussing locking) the camera will lock (i.e. store, until the button is released) the best values for the composition at the moment it is pressed.
As you are mentioning that the issues mostly occur when you are working in low light, I would guess that there could be different reasons:
- the locked exposure requires a too long shutter speed, causing movements of the camera to to blur the picture
- the locked exposure (also) requires the aperture to be wide open, so that you have only a very low depth of field
- focussing requires some light for the camera to be able to properly focus (at max. aperture) - in very low light situations the camera might not be able to properly focus.
If you could provide a capture taken, including its EXIF data, then we might be able to better help you.