Technically it's not an LMP it's a GT, but the one in GT5 is supercharged and doesn't respect any GT regulations. The real car took part in FIA GT in G2 and GT2 class, from 2005 to 2008 and some endurance events.
I can't be 100% sure but I think it actually raced in either the GT1 or GT2 class it Le Mans, Basically a race version of a production car like the Lister storm