AIN EL-HILWEH REFUGEE CAMP—Inside Lebanon's largest Palestinian refugee camp, disaffected and unemployed youth are increasingly joining radical Islamist groups fighting in Syria, saying it gives their lives a sense of purpose.

The growing hold of the jihadists is evident on the street at the camp's entrance, lined with flags of al Qaeda-linked groups that operate in Lebanon or Syria. Homes on Tawareq Street are pockmarked by bullets and rocket-propelled grenades—scars of recent fighting between Islamist militants and the Lebanese...