Wikipedia -- A baserunner is said to be left on base (abbreviated LOB) or stranded when the half-inning ends and he has not scored or been put out. This includes a batter-runner who has hit into a fielder's choice, causing another runner to be put out as the 3rd out.[5] If, during the final half-inning of a walk-off game, a batter hits a game-winning single with the bases loaded to break the tie, any men left on do not count as LOB in statistics.
So no, Boston did not catch up on LOB