webwork 2.13 works well on ubuntu 18.04 so I am pretty confident that
webwork 2.14 will also work well.
I would upgrade Ubuntu first since that is more complicated. Others with more systems admin experience than I might like to chime in on this advice.
After that upgrading webwork from 2.13 to 2.14 is relatively simple. A few pull requests and possibly adding a few CPAN modules, depending on what is currently installed on your machine. While there have not been changes to the configuration files in this last release I would do a review of your configuration files anyway in case you missed turning on (or off) some features that have been added since 2.11.
The release notes are here: http://webwork.maa.org/wiki/Release_notes_for_WeBWorK_2.14