To install latest kernel from Ubuntu 16.04 on Ununtu 14.04 LTS, run

sudo apt-get install linux-image-generic-lts-xenial linux-generic-lts-xenial

Before upgrade

root@server2:~# lsb_release -a
No LSB modules are available.
Distributor ID: Ubuntu
Description:    Ubuntu 14.04.5 LTS
Release:    14.04
Codename:   trusty
root@server2:~# uname -a
Linux server2.hostonnet.com 3.13.0-83-generic #127-Ubuntu SMP Fri Mar 11 00:25:37 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
root@server2:~# 

After upgrading kernel to latest Hardware Enablement Stack (HWE)

root@server2:~# uname -a
Linux server2.hostonnet.com 4.4.0-38-generic #57~14.04.1-Ubuntu SMP Tue Sep 6 17:20:43 UTC 2016 x86_64 x86_64 x86_64 GNU/Linux
root@server2:~#