Saving files in Lightroom and computer

Treat yourself to an external hard drive (which are incredibly low cost these days) and set the Lightroom preferences to store your originals on that external drive. Otherwise you'll find youself spending so much time trying to manage the space on your two small internal drives.

Lightroom Desktop will store the images in the Cloud, not on your computer. Once syncing to the Cloud is complete then they can be deleted from the computer (although it's always worth keeping a back up somewhere).

However, even though Lightroom stores photos in the Cloud, it does keep some locally also within its cache (recent imports and edits etc)

If you have a small SSD it may be worth reducing the size of this cache in the Preferences:

https://helpx.adobe.com/uk/lightroom-cc/using/preferences.html#:~:text=Adjust%20preferences%20in%20Lightroom,required%20preferences%20and%20click%20Done.