Did the Lebanese Kurds have to flee to Lebanon because they were Kurds?

There is the Mhallami ethnic group from Turkey in the Kurdish city of Mardin, who are also called Mardellis, also known by the extended families El-Zein, Omeirat, Remmo, Semmo, Miri etc. They are Lebanese Kurds because they fled from Mardin to Lebanon, but did they have to flee because they are Kurds and the Kurds…