How can I edit a Custom Label in Production Org where the custom label is protected and belongs to a managed Package. The documentation on Custom Label says that it is not subscriber editable if it is marked as Protected.
Yes, The documentation does say that managed package custom Labels are not subscriber editable, and in a way that is correct. But you can OVERRIDE the custom label with the new value in English language(*if that is your language) using Translation Workbench. There is a difference between the work edit and override.
For simpler understanding refer to the following link; else continue reading the comment.
https://help.salesforce.com/articleView?id=sf.cl_translate_edit.htm&type=5
Step 1 : Enable Translation Workbench for your org.
Go to Setup -> In Quick find type "Translation" -> Select "Translation Language Settings" -> Click "Enable" button.
Step 2 : Add a language (*for Example English) after enabling Translation Workbench.
In the same page "Translation Language Settings" click on "Add Button" -> For the first time by default English will be selected and Active checkbox will be/needs to be marked as true; else select a new language -> In the "Identify Translators for this Language" section add yourself in the Selected List -> Click "Save". Now English language can be used to override values using Translation workbench.
Step 3 : Override the value in the Managed package Custom Label to be referenced in Apex class and Client-side Javascript .
Go to Setup -> In Quick find type "Custom Labels" and select "Custom Labels" -> Select the Managed package Custom Label that you need to OVERRIDE(*not edit) -> In the Translations related list, click New to enter a new translation -> Select the Language you are translating into (* right now English as you have added this one in Step 2) -> In the Translation Text field, enter the translated value. This text overrides the value specified in the label's Value field when a user's default language is the translation language for both Apex class and Client side -> Save your changes.
(N.B.: The main purpose of custom Labels in my opinion is for UI and not Apex classes)