In 1971, LSU lost their opener to Colorado and lost to Ole Miss the week before Bama game. Last time both were undefeated was in 1973 when both were 9-0. In 1972 Bama was 8-0 and LSU was 7-0. In 1964 Bama was 7-0 and LSU was 5-0-1 with a tie with ut. Prior to 1964, if and when Bama and LSU played, it was usually the opener or second game of the season so I did not include those games in my search. Bama won all three years mentioned,winning the NC also, in 1964 and 1973.