The word "rivalry" in the context of college football means to me at least three things: (1) the two programs have been playing each other more or less continually for multiple decades; (2) there is relative parity between the two programs (i.e., in terms of championships, bowl wins, winning percentage, and national recognition generally.); (3) the two fan bases genuinely dislike each other. LSU qualifies on criterion #1. Regarding criterion #2, the matter is, I suppose, debatable. According to College Football Data Warehouse, LSU ranks #9 on the "All Time Team Rankings" list. (Alabama is ranked #1.) Since Tennessee is ranked # 10 on the same list and nobody would dispute that Tennessee is Alabama's rival, I will give LSU the benefit of the doubt on criterion #2. Regarding mutual animosity between the respective fan bases, my criterion #3, I do not think that LSU qualifies. LSU fans are, in my opinion, more humerous than hateful.