If you need to install this version of Mac OS, there’s a lot of wrong and bad information about this topic being generated by AI and Google links. The best and working method is shown in this YT. This approach creates a Thumb Drive that books into the same screen as MacOS Recovery and you select the reinstall MacOS option.
Have tested this approach for both Lion and Mountain Lion. Also, this does not work with Sierra, which has the new createinstallmedia structure: