This is another of those “helping somebody google this less than I had to” articles.
I’ve a Dell XPS 13 (the 2016 version) and since I started to use it with a LG 24UD58 4K monitor I noticed that things we not as smooth as I liked. Running (Linux, of course) xrandr I noticed that the monitor was running at 30FPS and there wasn’t an option for a higher framerate just as it was for lower resolutions.
After some trial and error I found how to get 4K@60FPS with this monitor and laptop:
You need a cable compatible with Thunderbolt 3. In my case it was a USB 3.1 to HDMI cable. Make sure that the specs show clearly that it can do 4K at 60FPS. I got this one on amazon.com (amazon.es link) which also have a USB C to female HDMI version.
You need to enable, in the monitor settings (small button below the LG logo) the setting “Ultra HDMI Deep Color” under in Picture -> Picture Adjust .
Connect and disconnect your cable, or better, reboot, and 4K@60FPS should be available.