The lateral motion is used when playing across lines that rise in sequence in intervals, such as the alberti bass, or any deviation of it such as broken chords, arpeggios...
Should fingers be curved?
Though it does depend on the piece, lateral motion of the hand would most likely move faster and have more stability when the fingers are out rather than inward. If the tips of the fingers are aimed at a relaxed angle, the distance between the tips of the fingers, for example from 2nd to 3rd finger tip, lessens. This means the notes are more likely to be the ones you aim to play, and it is more likely to feel sturdy and secure.
What is the Angle of the Hand from the Body mean? And Why Should We Pay Attention To Where We Place it?
Repeated chords at syncopation can be a real difficult task. Rather than having a secure and solid sound, the notes might be in danger of being light and shallow. Even when the notes are played correctly, the sound quality of these chords can be 'surfacey', rather than with a solid core. Therefore, the angle of the hand and the use of the flatter flesh of the finger tips is important.