It was founded by people from Tyre which is indeed in Lebanon.
After gaining independence in the seventh century BC, Carthage gradually expanded its economic and political hegemony across northwest Africa, Iberia, and the major islands of the western Mediterranean.
In 146 BC, after the third and final Punic War, the Romans destroyed Carthage and established a new city in its place. All remaining Carthaginian dependencies, as well as other Phoenician city-states, came under Roman rule by the first century AD.