I have a ThinkPad T440 with only Fedora installed. The UEFI-version I had installed was version 2.32, which I installed almost a year ago. Since then several new versions have been released, where 2.36 is the very latest when typing this. The following steps are what I did to update the UEFI/BIOS on my laptop.

Be warned though, you might brick the computer and/or void its warranty. This worked for me, but I cannot guarantee it will work for you.

  1. Visit Lenovo's support page and download "BIOS Update Bootable CD." In my case, with 2.36, it is called gjuj23us.iso.

  2. Download geteltorito.pl:

    $ wget http://userpages.uni-koblenz.de/~krienke/ftp/noarch/geteltorito/geteltorito.pl
  3. Extract from the .iso-file a USB compatible image:

    $ perl geteltorito.pl -o bios.iso gjuj23us.iso
  4. Write the image to your USB stick:

    $ sudo dd if=bios.iso of=/dev/sdX bs=512K

    WARNING! Be very careful with what drive you write to, i.e. sdX! It will completely overwrite all partitions on that media, so make sure it is not your OS, backup HDD, etc.

  5. Now reboot the computer, press F12 at startup and choose to boot the USB stick. You will now enter the UEFI/BIOS updater. Follow its instructions and read the information pages carefully.

  6. Done!

Visit this page and this page for additional information. Those are the two sources I used.