My assumption is that his vL rating of 88 would be modified by the pitcher's vL split when determining the outcome of a plate appearance. LH pitchers are generally tougher on LH hitters than are RH pitchers, and that's reflected by the pitcher's splits.
I further assume that there is no specific "penalty" built into the engine for same-handed pitcher/batter matchups. It's all done by individual splits for hitters and pitchers.
So it really all depends on the quality of LH pitchers vs RH pitchers that he faces during the season.