It is HIGHLY unethical for a program to demand that you reply before April 15- in fact this is one of the worst things that they can do other than reneging on an offer of admittance. The whole reason why the agreement was put in place was to enable students to compare funding offers. Even if a program (for example, a Canadian school) is not a signatory, they still know about this and If they are demanding a response before it is a cynical abuse of the system. Those that do are not respected by other programs. Frankly they have put a bullseye on themselves by doing this.
What you should do: contact the programs you have been accepted to (perhaps start with the one where the Dirextor of Graduate Studies has been most friendly/helpful/in contact) and tell the DGS what LSU has done. If you you are doing/did your undergrad at a research university talk to your department's DGS in addition, though it would be less hard to trace if it came from one of those other schools if you have any interest at all of attending LSU. The DGS will email their counterpart at LSU or ask their graduate dean to contact LSU's graduate school to get this rogue department to quit it. If you have been compelled to accept this offer before reading this you are perfectly within your rights to withdraw and accept elsewhere since they coerced you to do so under false pretenses in the first place; again whichever dept. ultimately offers you the most money and/or best program could facilitate this if need be. Once a program transgresses this agreement a prospective student owes them nothing- no other institution would shed a tear for them- just protect yourself. The bastards.