The new Partially Locked Application feature is only available when the user chooses the Generate XML action. It is not available in the Publish or Push Updates processes. Using Generate XML to publish/update apps works good for smaller customer bases, but quickly becomes impractical as the customer base grows.
Please use Page Editor on your "Publish Application" page and add "Lock Status" field to that page.
OK, I have that control on the publish page now (although it was called IsManaged on our server), but I am still not given a method to specify the Lock Status of each object (like the checkboxes in the Application tree shown on the Generate XML Page.
Try publish app and edit it from Master zone.
I'll enable Application Tree component on portal in the next release.
Fixed in 3.8.0 release