I had multiple problems with installing ubuntu/xubuntu 14.04 on this laptop (Thinkpad t440p gt730m).
I was able to install ubunut/xubuntu by adding option
nomodeset to install option - see example link: How to set nomodeset GRUB2 before I've installed Ubuntu
Unfortunately, after boot I wasn't able to use graphics properly (drivers were unable to load). Finally I found that there's problem with BIOS which may even lead to data corruption, example link - https://github.com/Bumblebee-Project/bbswitch/issues/78
So I decided to downgrade my BIOS to version 1.14, which is last known to be working properly BIOS version. After flashing BIOS (you will find instruction in link above), Ubuntu 14.04 installed without any issue, and 3D acceleration was enabled out of the box. I decided though to install nvidia prioprietary drivers (using simple 'additional drivers' utility) and now everything works like a charm (even ultra dock station :D) - I'm using nvidia-prime to switch graphics.
Hope lenovo fixes the BIOS problem in next version!
edit: After downgrading BIOS, Ubuntu will boot/install without editing boot options (that is, you don't need to add
nomodeset option anymore)