This applies if the "locked profile" belongs to a public figure (blue tick). Facebook allows limited downloads from their "Page" counterpart.

Use your phone's gallery app to crop the screenshot to just the cover photo area. : Open the profile in a web browser. Right-click on the visible cover photo thumbnail.

: A specialized viewer where you paste the profile link and click "View Locked Picture" to access the hidden image. Method 3: Third-Party Download Managers