No, they don't have to be at the top of the lineup. This is an archaic way of thinking. Speed at the top is outdated, a philosophy from the era of baseball that overvalued certain skills that didn't correlate to scoring more runs, an era when many thought it was better to put the ball in play, regarless of the result, over taking a walk. You need guys who get on base in front of your best hitters. They aren't getting on base. That said, you also need your best hitters to play to their talents, and over 16 games, Gonzo and Youk haven't done that. So it's more than who the Sox have hitting at the top of the lineup.
And, it's BS that the Yankees never seem to have these problems. In the last decade, the Yankees have been notoriously slow starters relative to their overall final record.