The lateral componant was to pull the capsule out of the flightpath of the rocket. The total accleration of the tower+capsule was miniscule compared to the rocket overall. If it didn't move left/right a bit then the rocket would easily catch up.

The thinking at the time was that, without the capsule attached, the tower might not fly as planned. It could be unstable in the thin up atmosphere. It might spin. That lateral thrust, withough the mass of the capsule, might cause it to spiral, leaving it floating out in front of the accelerating rocket.