I have a brand new ThinkCentre M720T (i3-8300) connected to a new LG 29WK600-W via DP->HDMI cable.
The ideal resolution for this monitor is 2560x1080 but both the generic Win10 graphics control panel and the Intel UHD graphics control panel are topping out at 1920x1080 (even when using the custom resolution option).
The spec sheet for this machine found in the "Specifications" section at the bottom of this page
indicates it supports resolutions up to "4096x2304 (DP)@60Hz; 2048x1536 (VGA)@50H."
The graphics driver on this machine is currently 220.127.116.1187. I have run Lenovo's update (indicated this was the latest driver) and have attempted to update to DCH 18.104.22.16819 using the .exe file from Intel's website. The latter errors out with a message along the lines that my PC manufacturer does not support / recommend this driver so it fails to install.
What do I need to do to get my machine to output resolution at 2560x1080?!
When using a hybrid laptop (i.e. one that utilizes both the Intel HD Graphics engine and a NVIDIA/AMD HD Graphics engine), you should only be using drivers from the laptop manufacturer (in this case Lenovo). To support laptop-specific features - brightness, backlighting etc. and especially to support switching between engines - manufacturers have to modify the generic drivers from Intel and NVIDIA/AMD to provide this support. When you install the generic, unmodified drivers from Intel (or NVIDIA/AMD), you will be missing this special support and features will stop working. It's probably a good thing that the DCH driver refused to install...
As for your resolution question, this is also controlled by the manufacturer, so you need to be talking to Lenovo.
One thought: have you downloaded and installed the monitor configuration file from LG? LG calls this a "driver"; it's really not.
Here's link to save you time: https://www.lg.com/us/support-product/lg-29WK600-W.