Ubuntu will display that message if the file
/var/lib/update-notifier/hwe-eol exists. I've seen a few reports that it isn't being properly updated after people upgrade their kernel version. You can safely remove that file. It will be recreated on a reboot if you indeed still have the have the old kernel in use.
If that's the case, make sure you've set the kernel in the DigitalOcean control panel to match the one that is installed on the droplet. The virtualization that we use requires that a matching kernel be found installed in your libraries in the OS and is also found on the hypervisor settings for your droplet, which is set through the control panel.
uname -r tells you the version the control panel is using
ls -lah /lib/modules shows you the libraries you have installed
To change it in the control panel, you need to poweroff the machine. Then go to the control panel, click on the droplet, click "settings" and then "Kernel". Next click the list and find the right version that matches your kernel libraries .e.g *Ubuntu 14.04 x64 3.13.0-30 Finally boot the droplet using the control panel.