Depends of the individual situation of both animals. In a ideal fair confront, with both in idal health conditions, lions would have some advantage. They hava sexual dimorphism due to sexual selection, what made of them natural born fighters, more than hunters. Tigers, in the other hand, are not gregary and male tigers must hunt by their own much more than a lion have in his entire life, they are much better adapted, both physically and instinctively, to hunt than to fight, inter or intraspecifically. Lion's mane not only makes them look bigger, but also is a effective protection from paws and teeth, and they use to fight against each others, once when they're nomads trying to conquer they pride, and once again in defense of the conquered pride against the new generation of nomads.
I've seen a site about it, it had some related accounts of fights between both species, but was hard to measure due to uncertain and unfair physical conditions, and sometimes, unfair disputes, such two tigers (one, actually a tigress) against a lion. This thing about the sexual dimorphism was shown to be true. Tigers or tigresses against lionesses, in the other hand, won more oftenly, if I recall.
May be surprisingly that the best tiger against lions was not the siberian tiger, the biggest of all natural felines, but some indian tiger, not much bigger, if not smaller, than a lion. Seems that the higher demographic density in this race produces more agressivity due to hormones.
Other interesting thing I've found in this site, but not about this fight, is a interbreed of both species (another kind of confront). A tiger and a lioness produce a "tion", a almost dwarf mix between both, maneless, and with shorter lifespan, and somewhat weaker than what would be expected from a proportional reduction. A lion and a tigress produces a "liger", the largest living feline possible, even larger and heavier than siberian tigers. Really huge. There are some individuals in circuses. They are also maneless, but sometimes with a tiny mane, and they have some dots or stripes, but not black, but almost the same color of the rest of the fur.
Only the females of this interbreeding are fertiles, and not allways, if I recall.