There are usually several "longterm maintenance" kernel releases provided for the purposes of backporting bugfixes for older kernel trees. Many Linux distributions provide their own "longterm maintenance" kernels that may or may not be based on those maintained by kernel developers such as Ubuntu.
Any kernel released with Ubuntu's initial LTS release will be officially supported/patched by Canonical for 5 years.
So in other words, you have nothing to worry about and only compatibility to gain with your aging workstations.