The real question is, did they have tose, or did they lack tose?
They may not have needed the lactose enzyme to digest milk. Given the high temperatures of north Africs, it is entirely possible that milk stored in pots or leather or bladder pouches would have converted rather rapidly into a yogurt type food. This occurs above around 90 degrees F. I know, I have made yogurt. Lower temperatures will give you sour milk and then conversion possible to cheese.
I had a co-worker from Jamaica who was complaining of itchy irritated eyes. I thought it might be Vitamin A or riboflavin deficiency. When she told me she was lactose intolerant and did not use milk, I decided it was riboflavin. I told her to eat 2 servings of yogurt a day, and within a month her eyes were fine. Souring of milk uses up the lactose.
Another thing some of those people did/do is prick a neck vein of their cattle, extract blood and mix it with milk for a rich, high protein food. They were careful not to take too much blood.