I would suspect that the only way is to recover them from your backups into the same folder structure as before which will mean that when you open the catalog they will be there.
The first thing to check is to see if the images are still on your hard drive.
If they are, then as BKKDon suggests, you may need to restore a catalog from your backups if your current catalog no longer contains the image references.
My backup was listed as C:\bill\desktop\lightroom\backups
When I got there, it said "lightroom cannot use the catalog named
'lightroom catalog' because it is not writable and cannot be opened. this
could be causedby incorrect permissions or because other lightroom
application is using the catalog.You may try to correct the problem or you
may select a different catalog."
I found nothing.
You need to find the backups of your photos, as well as your backup catalog.
The backup catalog that you found can be moved (using your operating system) to a new folder, where you have WRITE permission, and it will open properly (or change the permissions in the folder that it is currently in).