re: Why did we never play Auburn before divisons?

LSU didn't play Georgia, Tennessee, Vanderbilt or Auburn very much during the time frame you reference. There were no conference requirements for the number of games played or how often you rotated member schools as opponents, if at all. It wasn't until 1982 that the SEC officially adopted a six-game conference schedule. As an example, LSU won the SEC in 1970 with a 5-0-0 record. Tennessee also played five SEC games but the rest of the league played six or seven regular season SEC games that year.