Should I continue experimenting or not?
It looks like two traces had their gold plating removed and one trace delaminated and is probably welded to the matching contact on the female receptacle.  This trace may still make contact, but not at the intended quality.  

It might be working because it still makes contact for the moment or it could be a standard multipin connector and that pin isn't used for the video standard your monitor is using(It's a 31 pin cable and you only need 19 pins for HDMI), or it's redundant, or only partially redundant (like an extra power pin that only becomes significant at a certain load).  If this cable is the sole connection for the monitor panel of your laptop, it would include pins for the other functions of the monitor (are the LEDS if any and webcam working?) and you may simply have not detected what's wrong yet.

Just speculation, but I would monitor it in the future and if it becomes unreliable, or intermittently stops working when you jiggle it or when it warms up or operates at high brightness, you should remember this problem.

It wouldn't be a bad idea to look for a repair guide for your laptop.  If you can find the pinout of that connector or the name of the cable, it would be much easier to be certain what the missing pin is intended to do.  

Some laptops, particularly Apple's are designed specifically to prevent or discourage user disassembly and repair, but most are not.  The general rule when disassembling an unknown laptop is to find the screws you might miss (because they are hidden behind a battery door, a sticker, a rubber footpad, a piece of plastic flashing, whatever) and make sure you are prying things apart in the correct directions with a suitable tool so as not to damage small plastic parts that you would be unable to repair.  It is your skill and preparation that will determine whether on average you damage things enough to not make it worthwhile and practice makes perfect if this is a skill you want to have.  I would take it apart just to clean it if I wanted to.

Personally, I'd try to find enough information that I could repair it myself, but be warned you may have to spend quite a bit of time searching to find the information you need.  There is also a chance that someone on here will know what that pin is for or how to look it up, so best of luck.

You also need to check for damage on the other side of that connector and you might want to check if the cable is hardwired to something on the other end.  If it's not it may be an easy replacement once you find a suitable part.

By the way, it looks like Lenovo is friendly to at least some consumer repair, so you could start by going on their website to look for documentation.