With an annual plan that's monthly or yearly paid you can't suspend.
With a month to month plan you can, but but this plan is much more expensive.
Read more: Legal subscription terms | Adobe
Are you talking about Lightroom Classic CC or Lightroom CC? These two are different (despite the similar name) and have different amounts of cloud space. Lightroom CC vs. Lightroom Classic CC | Adobe
I do not think you can suspend your subscription, despite what was said above. Lightroom Classic CC can work with your photos while offline (I don't think Lightroom CC can work with your photos while you are offline ,but I'm not sure.)
>I don't think Lightroom CC can work with your photos while you are offline ,but I'm not sure.
It can if they have been downloaded before (or are still on the drive because you imported them on the same machine) and are in the local cache.
For most people Lightroom Classic is the right solution and you can play a bit around with syncing files from Classic to CC or vice versa. Lightroom CC is the right solution if your needs are very modest - i.e. you don't need to print, watermark, have hierarchical keywords, control your exported files, publish to non-adobe web services or any of the 100's of features in Classic that CC misses.