Your LVM-Volume Group is just within the sda5 partition, and this partition is 79.5 GB, so I would say that your volume group is just full. And you have no space left to increase your logical volumes (especially vg_ucs-root). Ideally you have always a bit of spare, so you can adjust the logical volumes.
For the df output, there are a few explanations:
I think there are way to span volume groups over several drives, I suppose in your case the sda-drive is a fast SSD drive.
I’d see to check what takes up the nearly 80 GiB of space, and if you don’t have ways to reduce that.