Apparently, scientists now believe that because the famous giant "sabers" were actually quite fragile, Smilodon had some form of sheathing to protect its large and fragile teeth, which were likely in the form of big lips. Whether it was the upper or lower lips is unknown, but it's likelier that it was the upper lips that sheathed its giant "saber teeth".
Not the case in the games and movies the Smilo appears in. No offense, please, most people often give it the regular lips to make it as menacing as ten tigers.