1. make sure your server system up-to-date as follows
    $ sudo apt-get update && sudo apt-get dist-upgrade

  2. reboot
    $ sudo reboot

  3. install the update-manager-core package using the command below that is if it is not yet installed on your server:
    $ sudo apt-get install update-manager-core

  4. After that, edit this file, /etc/update-manager/release-upgrades using your favorite editor and set Prompt=lts as in the output below:
    $ sudo vi /etc/update-manager/release-upgrades

  5. start the upgrade process as follows:
    sudo do-release-upgrade -d

Reference:
http://www.tecmint.com/upgrade-ubuntu-14-04-to-16-04/#ubuntu-14-04-server