S1: What is especially noticeable about the pair is that they always dress impeccably. S2: Lunch is served late in the office, specially on days when there is a board meeting.

'Especially' means particularly or above all, and is used to single something out for emphasis. 'Specially' means for a specific purpose. In S1, 'especially noticeable' correctly uses 'especially' to emphasize the notable quality. In S2, the intended meaning is 'particularly on days when there is a board meeting', which requires 'especially', not 'specially'. Hence S1 is right and S2 is wrong.