Gunmen fired on a government checkpoint near the Syrian border.
Fighting in neighboring Syria has drawn Lebanese districts into conflict.
The sectarian violence in Tripoli is being described as the heaviest in years.
The deaths raise to 31 the number of fighters Hezbollah has lost in the struggle for the town of Qusair since Sunday.
Syria and its patron Iran have hinted at possible retribution for the strikes.
Suspicion fell on Lebanon's Hezbollah militant group.
Tuesday's rocket attack came hours after two leading Lebanese Sunni Muslim clerics called for holy war, or jihad, in Syria.
Syrian forces launched a counteroffensive aimed at regaining control of territory around the country and along strategic border areas.
The United Nations gave its starkest warning yet that it would soon run out of cash to cope with the vast influx of Syrian refugees.
This is the first such shipment by Moscow which has supported President Bashar al-Assad throughout the two-year-old conflict.