Interesting. My strategy against most lefties is to go to the forehand as much as possible and just hang out in the ad court and dare them to go up the line. Lefties tend to like to angle the forehand. The backhands tend to have more variety of location. That being said, if the person has a much weaker side, why wouldn't I just keep hitting the ball to that side until it breaks down?
If I was the lefty and I wanted to protect my backhand, I would not recover to the middle at the baseline. I would keep the forehand side open enough that it would just make sense to go to the open court and try to run around shots hit to the backhand side. Also, I would try to use backhand slice down the line low to and force them to hit up, hopefully going to my forehand at some point. I would also have tried moon ball. Looping a ball up really high makes it harder for the opponent to go down the line and will also give you more time to get into position.
Ex-Coach: U of Delaware & Drew U. Pro Kennex Ki-5(R) & Gamma RZR 98 (L)
Dunlop Black Widow 17 (63lb) Babolat N.Vy 16 (64lb) USTA 4.5.