In the last 20 seasons, there have been 138 Opening Day games started by left-handed pitchers. Randy Johnson has 14 himself, followed by Mark Buehrle with 8. There have been 444 Opening day games started by righties, led by Roger Clemens with 10 and Brad Radke with 9.
That works out to 23.7% of games started by lefties.
Over the same 20 years, looking at all games (not just Opening Day), lefties have started 25,906 games and righties have started 66,514 games. That's 28.0% of games started by lefties.
That means that lefties are a bit less likely to start on Opening Day than on other days. In turn, this might simply mean that over the last 20 years, there have been a few extra right-handed ace pitchers that have prevented lefties from taking some of those #1 turns.
Going back to 1919 (yes, our box scores go back to 1919 now!) the numbers are:
Opening Day: 508 starts by lefties, 1,444 starts by righties (26.0% by lefties)
All: 88,743 by lefties, 218,857 starts by righties (28.9% by lefties)