The documentation does not mention specific Linux distributions. LiCBAS uses bash shell scripts and Python 3.6 or later. These generally present few differences across a wide range of Linux distributions.
You may, however, encounter problems with the support for some PC hardware. Graphics and network hardware sometimes present problems. You may want to look for other linux users with the same hardware to help figure out if there are issues that would affect your use case. The LiCBAS installation documents give examples for Anaconda Python, which is available for many linux distributions, but most recent Linux releases will have Python 3.6 or higher. You will probably have to install some of the requirements. If you are new to linux it is wise to ask around to see what others at your institution use. Many linux users are happy to help new users get off to a good start.