Yes. But in order to do so, you have to pay between $18 and $33 to upgrade the ticket. This must be done no later than 5PM on the Friday before the game.
The site states:
STUDENT UPGRADES (LSU student to Guest or non-student)
ALL STUDENT UPGRADES END AT 5 PM ON FRIDAY OF EACH GAME WEEK.
Student tickets can be exchanged so that a non-student may sit in the LSU Student section.
The cost for the exchange is $18 for Reserved tickets and $24 for General Admission tickets ($27 & $33 for the Alabama game only).
Upgrades for future games can take place anytime prior to game week.
Tickets used for upgrades do not need to be transferred and may be brought in by anyone.
Avoid any potential lines - upgrade or transfer tickets in advance of Friday