A lefty hitting a crosscourt forehand seems to get a little bit more penetrating side spin than does a righty hitting the same shot. Also, the most important factor is the serve. The lefty has what seems to be a more natural slice serve although the kick is not as useful.
Considering this, how do you serve a left handed tennis ball?
Left-handed players can serve out wide when on the ad side of the court to swing the ball to the backhand of the righty. From there, the righty is put at a disadvantage and the lefty is able to dictate.