The raid on a house in the Al-Tabbaneh district of Tripoli aimed to capture Hajjar Al-Abdullah, but was met with resistance including gunshots and hand grenades, the army said on its website.
In the fighting, Abdullah and a soldier were killed, several other soldiers were wounded, and Abdullah’s brother, Bilal Al-Abdullah, was detained. The army seized money, arms, ammunition and other military hardware from the house, it said.
Lebanese authorities say they have disrupted a number of Daesh attacks and networks since the last major attack — a 2015 twin suicide bombing in Beirut.
Lebanon has mostly escaped the rash of militant assaults around the Middle East spurred by the war in its neighbor Syria, and last year forced Daesh fighters out of an enclave on the mountainous border between the two countries.