What kind of oath is this, and is expiation obligatory after admitting to a lie?

The oath you swore while knowing you were untruthful is called an oath of immersion (yameen al-ghamūs), and it is one of the major sins. It is called "immersion" because it immerses the swearer in sin in this world and in the Fire on the Day of Judgment. The oath you uttered pertains to a future matter, and therefore, it is considered a binding oath (mun'aqidah) for which an expiation (kaffarat yameen) is required. You are obligated to repent to Allah Almighty and to offer the expiation for the oath.