Yikes! It’s scary to possibly lose data. I’ve been in this situation and may be able to help.
In this case, the reported error message is a permissions issue.
I know of two things you can try in order to override permissions on this volume.
Option 1: Disable Permissions:
Use “Get Info” on the troubled drive (in this case “Untitled”) to enable “Ignore ownership on this volume”.
This is a temporary change and is reversible. Requires unlocking first.
More Detailed instructions from Apple are here.
Option 2: Write Over the Permissions:
Caution: Proceed with care. If you don’t know what you’re doing, don’t try this on a bootable volume.
You can change the permissions to “Read & Write for everyone” and apply those settings to all enclosed items using Get-Info or with the CHMOD command via the terminal.
More detailed Instructions are clearly written up on HowToGeek here.