If you run Gnome or KDE Plasma as your desktop environment, there are built in tools for you to calibrate your screen. You just need to find an .icm or .icc profile file that matches your screen to calibrate it. The best is to make one yourself with a hardware calibrator, but if you do not have a calibrator you may get close by using a profile another user of the same screen has made even if it will be slightly less accurate. (See below to find one that matches the X230 with the IPS screen.)
I have run LXDE up to now and have just switched to LXQt. Neither of these lighter and smaller desktop environments have a built in screen calibrator, so I needed to find another solution. The solution I found will work in any desktop environment or window manager as long as you use X11.
On the Arch Wiki I found a good solution called xcalib. This is a command line tool that takes an .icc colour profile and calibrates the screen with it. I tried with the .icm profile I had extracted from a Windows executable supplied by Lenovo on their site and it didn't work. I then DuckDuckWent and found on a Thinkpad forum that there was a colour profile for the X230 available in the Display section of a review of the X230 on notebookcheck.net. The profile is hidden on the bottom of a table with technical info on the right of a picture with the text "distribution of brightness" underneath. (If it should ever disappear, contact me through my contact page and I will happily email you a copy.)
I downloaded the .icc profile file and fed it to xcalib and the colours changed. I also have a Thinkpad W520 with a calibrated screen and know how my pictures on Flickr should look from seeing them on that screen, so I took a look at the same pictures on the X230 screen and they looked as they should as far as I was able to ascertain. It was really obvious that they did not look right before the calibration, but after the calibration, they looked alright.
To make this change permanent, all you need to do is to execute the xcalib command with the .icc profile file that fits the screen at the start up of your desktop environment or window manager. In LXQt, you can use the Session Settings to autostart xcalib thenameoftheprofile.icc. In LXDE, you can use the LXsession session manager to do the same. I put the .icc profile file in my home folder to be certain I back it up properly.
To me, getting the screen calibrated was the one missing piece to make the Thinkpad X230 an excellent ultraportable machine that can replace my Thinkpad W520 as my main machine. I like the small and light 12 inch form factor, the IPS screen, the excellent keyboard, the relatively powerful i7 M-class processor, the long battery life and the generous selection of ports.