It is definitely possible for a lion to beat a tiger in a fight. However, the tiger has often proved victorious throughout history — lions and tigers were used as a form of entertainment by the Romans, who pitted them against each other in the Colosseum.
Each animal has its own set of advantages and disadvantages in a fight. Of course, factors such as the strength, age and size of each animal will play a role in which wins a particular fight. Another factor to consider is that a lion is typically more social than a tiger, which is often a disadvantage.