I assume you mean disk space and not memory, you want to clear out some disk space on the internal disk. Is that correct?
If you have moved your photos somehow (this is not a backup), please follow these directions to reconnect the photos in Lightroom. Adobe Lightroom - Find moved or missing files and folders
By the way, you have to (it is mandatory) make true backups of your catalog file and photos, this mean exact identical copies, made by some automated method, and placed on a different physical drive than the originals. Lightroom allows you to make backups of your catalog file on a regular basis, this is an option under Catalog Settings. To make backups of your photos, you would need some third party software to do this.
>To make backups of your photos, you would need some third party software to do this.
This is sage advice. I'd recommend you buy another big external hard disk and set up the built-in OS X backup software - Time Machine, which is as much set it and forget it as it gets and very user friendly. You don't need extra software. Just make sure to make it also backup your external disk with photos (very easy to do in the system preferences). Most external hard disks that you buy nowadays come formatted for windows and you should reformat to the Mac's native format to use them as a backup disk.