Thank you for your reply!
If the axes used in Symmetry and Locking are the Local axes of my object, then do this mean that I am out of my luck to symmetrize or lock the global axes please?
you can keyframe different rotations
I am not sure what you mean by the keyframe. Let’s assume that after rotating the local axes, you keyframe it. Wouldn’t this rotation also rotate the object itself please? In other words, I don’t think it is possible to rotate the local axes without rotating the object itself. If the object is rotated along the local axes, then the orientation of the local axes remains the same with respect to the object, so I still can not lock any arbitrary axis. Right?
My rough idea about locking any arbitrary axis would be in the Object mode, and Shift + A to add “Plain Axes”. Then use these plain axes to define what exact axes I want Blender to lock. But I do not know how to let Blender use this empty axes, rather than the local axes.