Should the word be capitalized in this sentence family lived south during civil war?

Yes, the word "South" should be capitalized in the sentence "Family lived south during the Civil War."

Here's why:

* "South" refers to a specific geographical region in this context, namely the Southern United States.

* Proper nouns, including names of regions, are capitalized.

The corrected sentence should read: "Family lived South during the Civil War."