What is the ruling of Islamic law on lying about one's place of residence to facilitate legal procedures when reporting the theft of a car license plate?

The default ruling for lying is prohibition. It is defined as informing about something contrary to its true nature. However, it is permissible if there is a legitimate interest, such as preserving a right that cannot be achieved except through it, or in war, or for reconciling disputing parties, or with one's wife, or to save an inviolable life from perishing, provided that it does not result in harm to others. If allusions (ma'arid) can be used instead of outright lying, then their use becomes obligatory. As for the "al-Yamin al-Ghamus" (a false oath sworn by Allah concerning a past event), the majority of scholars hold that no expiation is required for it because it is too grave to be expiated.