In my opinion, I would say that Baroka is the "winner" in the play because he successfully woos Sidi and ends up marrying her. Throughout the play, Lakunle and Baroka both attempt to win Sidi's favor in order to marry her. However, after Sidi's images are portrayed throughout a foreign magazine, she becomes extremely conceited. The Bale understands that Sidi is vain and devises a plan to sleep with her. He tells one his wives named Sadiku that he is impotent, knowing that she will spread the rumor. Sidi believes the rumor and visits Baroka's home to mock him to his face. When she arrives at the Bale's home, he shows her a machine that makes stamps and promises Sidi that her image will adorn each letter leaving the village. He then impresses Sidi with his wisdom and sleeps with her. In the end, Sidi tells Lakunle that she decided to marry Baroka because of his youthful zest and masculinity. Baroka ends up the "winner" because he married the "jewel of Ilujinle." 

At least on a simple level, the Lion is the winner since he eventually wins the hand of Sidi, the woman for whome he and Lakunle are competing.  He has to try a variety of tricks before he is able to finally convince her that she ought to accept his proposal, but in the end, his final ruse succeeds.  Lakunle is very well spoken but lacks the ability to follow through on much of what he says, eventually helping Sidi in her decision to marry the Bale.