When was the explosion of the IDF military headquarters in tire during the first Israel-Lebanon War?

YES. The two suicide bombings against the Israel Defense Forces' headquarters building in Tyre, Lebanon took place in 1982 and 1983, which was during Israel's intervention in the Lebanese Civil War. This intervention is commonly called the First Israel-Lebanon War in Pro-Israeli circles (in contrast to the War with Hezbollah in Lebanon in 2006, which is called the Second Israel-Lebanon War).