XPS 15 L502x, 2K external monitor

First of all, when you say "2K resolution", what resolution do you mean, exactly?  2K is technically a film resolution of 2048x1080, but in the consumer world it is sometimes used to refer to 1920x1080, aka Full HD.  As a similar example, 4K is technically a film resolution of 4096x2160, but in the consumer world it can refer to 3840x2160, aka Ultra HD.  If you mean 2560x1440, that would be QHD resolution or 1440p.  Nobody refers to that resolution as 2K, at least not accurately.

If you mean 1440p, your issue is probably that the HDMI port on that system uses an older revision of the HDMI spec that does not support the bandwidth required for 1440p.  The maximum resolution you can use involves much more than just the GPU.  It also involves the connector you're using, the revision of that connector on both the system and the display side (some displays that can accept a certain resolution over DisplayPort can only accept a lower resolution over HDMI, for example), and the cable you're using.  In some cases, the total number of displays you're trying to use and their respective resolutions all come into play because there are limitations around the total bandwidth requirements for all of your displays, although I don't think that applies here.  Lastly, in your case I don't even think you're looking at the right GPU.  I believe the XPS L502X uses NVIDIA Optimus, in which case the NVIDIA GPU probably isn't physically wired to any of the display outputs at all.  Instead, it is probably operating as a render-only device and the Intel GPU is wired to the display outputs, in which case you'd need to see what the maximum resolution for that GPU is.

But again, this is probably an HDMI revision issue, in which case the answer would be to use the Mini-DisplayPort connector instead.  Since you didn't mention what specific display you're trying to use, I don't know what your input options are, but there are Mini-DisplayPort to HDMI adapters if needed.