Tiger wins 9 times out of 10
Lions let females hunt while they protect the pride against mostly hyenas.
Tigers are true killers. They are solitary predators that roam around killing all sorts of animals just to see if it can do it. Tigers like to test themselves even against much bigger animals. On top of that, tigers can get to be much larger than lions.
I think a better fight would be a grizzly bear or polar bear vs a tiger. Apparently the Russians say Siberian tigers hunt bears. I don't know what kind of bears those are though.
I've read little blurbs and seen video clips saying that the Roman's had animal fights to the death and the tiger was the king of that shit. Even against lions.