Moving this discussion to the Photoshop Lightroom forum.
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A Lightroom license, regardless of whether it is a creative cloud license or a standalone license, allows you to install Lightroom on two different computers for your personal use. You can install Lightroom on the new computer, and then follow these instructions on how to move or copy the files from your current computer.
Each installation of Lightroom must have its own local catalog on a drive that is local to that computer. Some people use dropbox for the catalog so that it can be used on both computers. There are lots of considerations when trying to work with different computers. But it can be done.
Thank you so much!