You can’t lock down a task due date. But you can:
- have a project called “locked dates”
- multi-home those tasks into the project
- have a rule that says “if due date change, then X”
X could be:
- comment they don’t have the permission
- assign to a manager
- mention a manager in the comments
- …
Does this help?
PS: if you make your project comment-only, only the assignee can change the date…