Do lefty batters like the low ball?

Maybe Pitch F/X has already answered that question.  Anybody know?  Most of my posts in February dealt with righty/lefty batting issues.  I looked at a differentiating factor seldom, if ever, examined: how batters throw.

For batters since 1901 with at least 5,000 plate appearances (PA):
- 99% of PA for righty batters: throw righty
- 42% of PA for lefty batters: throw lefty.

Yogi Berra

Since Mickey Lolich is the only pitcher I could find who as a child changed his throwing arm, I concluded that players can learn to bat the other way, usually righties learning to bat lefty, but their true handedness is shown by how they throw.  So, all lefty hitting catchers are really righties.  Supposedly, Yogi Berra did everything righty except bat; Yogi even golfed righty.

All of which has me wondering if that old adage, if actually true, might be explained by determining whether lefty batters who like the low ball throw righty.  In other words, there may be a reason that true lefty batters like the low ball more than righty batters.  Or maybe it's the opportunist lefty batters, those who throw righty, who like the low ball.

I do not have access to data on that level and cannot answer the question.  Anybody?