NOTE: If it tells you that you don't have "LFA '10", but you do, and you try to add it to the race week, you may crash the program.
I have no idea why that happens, but your workaround is to not add "LFA '10" to the race. If you want to use it in a race and you want to pick it from the list, turn off "Qualified Cars Only" and you'll be able to pick it from the list: