Well, right off the bat, you have the usual storage issue. As you correctly noted, 128 GB according to the manufacturer only translated to 119 GB when measured by the OS. However, the clue is in your "71 of 91 GB free". A lot of OEMs use a dedicated Recovery partition on the primary drive in place of the old physical discs; it saves on packaging, & GB storage is much cheaper on an SSD/HDD than on a set of CDs/DVDs. You can usually expect the OS to take up roughly 20GB on a drive, which means the recovery partition will also take up about that much space. And those are OS-measured GB, not manufacturer GBs. Sometimes, of course, the recovery partition may be even bigger.
So...in your case, fresh from the OEM you saw 71 GB free out of 91 GB available. That confirms the "20 GB for OS" rule...and points to your Recovery Partition measuring about 28 GB (119 GB - 91 GB = 28 GB), most of which would be the OS.
One way to double-check, is to see if there's a separate volume listed under My Computer (or whatever WIndows 8.1 calls it).
As for what your options are...you can always see about copying the Recovery partition onto physical DVDs, which might allow you to free up the space. However, I don't know how well those will work should you have to restore your PC, nor what might happen to any personal files (i.e. if it makes you blank the SSD to take advantage of the free space). Based on the brand (Lenovo), this is probably a laptop...which means the usual solution (adding a secondary HDD for additional storage) is probably not available. What you should consider is getting an external HDD (USB or eSATA, depending on what your laptop supports) to store the majority of your personal files -- homework assignments, photos, home videos, etc. -- that you a) don't use on a regular basis) and b) take up a lot of space. Also use it for programs that you use only occasionally, or that don't need the speed boost as much. Also, barring the installation of a larger SSD, you'll probably have to get used to the idea that you won't be able to install too many large apps (i.e. recent games) on the SSD, as they just take up too much space (if you only have 71 GB available, installing a game on your SSD that needs 60 GB of space for the uncompressed textures isn't very appealing).