I'm not sure that is the case. You will note that it refers to "academic, public relations, athletic, as well as other purposes not specified ...". We can continue to push the envelope, but we may be playing with a loaded gun. Why risk it? If we don't use athletically "University of" before Louisiana or "UL", are we violating the law. If we use only Louisiana and LU, it doesn't appear we have violated anything.
Here is what the law states:
"The use of the two-letter University of Louisiana abbreviation, "UL", and/or "U of L" are prohibited by the university or any of its affiliated organizations (alumni associateions, development foundations, bookstores, etc.). For academic, public relations, athletic, as well as other purposes not specified, the use of the University of Louisiana abbreviation must always include the abbreviation for the municipal location of the institution. For example, ULR is appropriate for University of Louisiana at Rayne."