Looking to Temporarily Suspend Account And Return In a Couple Months

I don't know if Adobe can put an annual subscription on hold.  The Photography Plan is an annual plan, not month-to-month.  So if you cancel now, it's gone until you re-subscribe.  Also cancelling your annual plan before the 12th month will incur a 50% early termination fee.   I realize that's not what you asked.  But that's generally how it works.    You can contact Adobe Customer Care directly and ask them.  But don't be too surprised if they can't do it.

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Not sure what you mean by "The Creative Cloud". Have you uploaded files to the Adobe creative cloud storage space they gave you with your subscription? And if you have exactly how did you do that, what method did you use.

If you mean all the EDITS you have done to images you have imported into LR then to Save those edits you need to Export those images to a New file. That will Burn the edits into that new file. LR Never changes the original image file. So what you are looking at in LR is the original image with the Edits Added To it but not really Included IN that file.

Other than that all your images are stored on your computers hard drive, or external drive.

Are you asking about LR Classic or the newer Cloud Centric (Based) Lightroom?

As for suspending your subscription. That is not possible that I know of. You can Cancel but doing so would incur a cancellation fee of 50% of the remaining subscription cost.