I had a similar problem where I was able to add space via a new PV to a VG, Yet df showed no increase in space. The solution for me was to extend an existing LV with:
$ sudo lvextend -r /dev/fedora_localhost-live/root /dev/mmcblk0p3 [NOTE: the LV & PV shown are specific to my installation]
When someone does an lvextend command the filesystem does not automatically get resized as well unless you use the option to do so. As a result commands to show the lv size will show the new size but commands to show the filesystem size will still see the old size.
The solution is to always use lvextend with the -r option which will do both parts at the same time. If you forget the -r option then you can do the filesystem part afterwards with resize2fs after the lvextend command completes.