If you have a lifetime licence for a specific version of TeamViewer, that licence will also allow you to use any previous versions of TeamViewer. If you have a licence for TeamViewer 13, you would therefore also be able to use TeamViewer 12, TeamViewer 11 etc.
That being said, TeamViewer 13 will of course also be available for Linux.
I hope this information helps. If you have any further questions, please do not hesitate to let me know.
All the best,
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