It doesn't quite work like that, Jim. Lightroom creates local copies of images in 3 circumstances:
1. The user requests that by checking the option to "Store a copy of all originals at the specified location". That ensures that all originasls in the cloud are copied and maintained in that specified location. The default location is the system drive, so if the drive is likely to be space-constrained it would be sensible to designate a different drive as the "specified location" before checking that option. Many users do enable that option as they think that can act as a backup, but the more pragmatic reason why a user might store that local copy of all originals is to ensure access to all images if using an unreliable or non-existing network connection.
2. Assuming that option is not checked, Lightroom will still copy all files being imported into the designated location, and it's those copies that are used for the ensuing slow upload to the cloud. Once that upload is complete, those local copies become eligible for deletion, but there are some complex rules which govern when they are deleted.....this results in the copies hanging around for longer than expected. Adobe are aware that they perhaps ought to be more aggressive in applying those rules so that the images are deleted in a shorter timescale. However, once the user is satisfied that those images have been successfully synced up to the cloud, they can be manually deleted.
3. Whenever Lightroom is online (which with the desktop app is likely to be the case more often than not), it will automatically download a copy of the original file from the cloud whenever the user starts to edit an image (even just zooming to 1:1 is sufficient to download a copy of the original). Once downloaded to the specified location, they become eligible for deletion using the same rules as the import copies. So again, they'll likely stay in that specified location for longer than the user may anticipate, but again they can be deleted manually if required. Personally, my specified location is on an external drive with adequate free space, so I've never had cause to manage (or even check) them manually.
When you delete images from Lightroom, they are not immediately erased but are instead moved to the "Deleted" container, where they will remain for up to 60 days. During this time they are available to the user to "restore" them in the event of a change of mind (or mistake), and also during this time the local copy (if one exists) is also not deleted until those 60 days are up. If the user wants to, they can delete the images from the "Deleted" container at any time during that 60 day period, whch will in should immediately remove the local copy.
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