liblightdm-qt-3-0 software package provides LightDM Qt client library, you can install in your Ubuntu 14.04 LTS (Trusty Tahr) by running the commands given below on the terminal,
$ sudo apt-get update $ sudo apt-get install liblightdm-qt-3-0
liblightdm-qt-3-0 is installed in your system.
Make ensure the liblightdm-qt-3-0 package were installed using the commands given below,
$ sudo dpkg-query -l | grep liblightdm-qt-3-0 *
You will get with liblightdm-qt-3-0 package name, version, architecture and description in a table
| Distro | Ubuntu 14 04 lts trusty tahr |
| Section | X Window System software |
| Package | liblightdm-qt-3-0 |
| Version | 1.10.0-0ubuntu3 |
| Description | LightDM Qt client library |
| Sub Section | x11 |