LSU football has only two penalties to it's name...

From another site:

LSU football has only two penalties to it's name: the tutor scandal in 2002 under Saban, and last year's McCarthy scandal under Miles.

The first of these, In 2002-03, LSU admitted to five secondary NCAA violations after an investigation into a plagiarism and grade changing scandal involving football players in a kinesiology class.

The NCAA accepted LSU’s self-imposed penalties of two lost scholarships and four recruiting visits during the 2003-04 recruiting year and later settled two lawsuits with the instructors who made the initial allegations.

The NCAA agreed with the school’s report that violations were secondary and not systemic.

No further NCAA sanctions for LSU - College football- NBC Sports

As for the DJ McCarthy violations, he was providing JUCO transfer Akiem Hicks with a reduced-rent apartment for 3 months last summer, improperly transporting him to LSU and making impermissible telephone calls to Hicks during the recruiting period.

Martin and Alleva have said the violations did not go beyond McCarthy and do not implicate head coach Les Miles.

LSU discovered and self-reported the violations on it's own, and suspended McCarthy from all coaching duties, especially recruiting.

Akiem Hicks had his scholarship revoked and never played a down at LSU. McCarthy's suspension is thought to have led to WR Justin Hunter's decision to switch his commitment from LSU to Tennessee.

The NCAA has yet to rule on this matter, but it's generally believed that since both McCarthy and Hicks are no longer at LSU, any penalties would be extremely light.

LSU reports NCAA violations

Those, in a nutshell, are the entire amount of penalties ever committed by LSU football. The only SEC football program with less penalties is Vanderbilt, with one.