Are you referring to the 8 year old version of Lightroom? If so that application has nothing to do with the cloud. It also may not run on a newer computer. Can you confirm what version of Lightroom you are using?
No migration is needed. Just install the Creative Cloud app on the second Mac, use that to install Lightroom, then when you launch Lightroom for the first time it will automatically sync with the cloud and download all the local content that it needs.