Right clicking copper items in the default game removes oxidation from them. Doing this to copper lanterns toggles them on and off instead. Right clicking copper lanterns with an axe should scrape off oxidization instead of toggling them on and off.

The default behavior when right-clicking is that you first try to interact with the block you are looking at, then with the item you are holding. You can see this when, for example, when right clicking on a chest whilst holding a block. It will open the chest rather than placing the block.
If you hold shift, the order is reversed, i.e. you first try to interact with the item you are holding, then with the block you are looking at. As the lantern has a regular right-click action, toggling it on-off, you have to hold shift in order to use an axe on it and 'scrape' it.