Goals from Lubambo and Winston Kalengo handed Zambia the home win and a 3-0 aggregate victory following a 1-0 away win on Wednesday in Karima.
Both goals came in the second period after the home side dominated the opening 45 minutes with Lubambo, Kalengo and Collins Mbesuma all denied by Akram Al Hiadi.
Lubambo scored the first goal in the 58th minute when Akram parried Kalengo’s header into the midfielders path.
Kalengo completed the business for Zambia in the 80th minute with a from effort to score in back-to-back games against Sudan.
Zambia now await the draws for the last 20 teams in the group phase that will decide Africa’s five representatives at the 2018 Moscow finals.