Exchanging into Pawn Ending?

This position arose in Lasker -- Tarrasch, St. Petersburg 1914, the source for Van Perlo 7 (see "Endgame Tactics").

Black to move

The game continued 37...Bxg7 38.Bxf5 Kxf5 39.Kxg7 a5, reaching the position where Van Perlo celebrates Lasker's "amazing escape" (Van Perlo's Endgame Tactics, 21).

White to move

White has a drawing combination

Did Black have something better?