Will lateral movements with my Ready Rig be equal on each side?

In your Ready Rigs normal setup, with a strap connecting to each support arm, yes. You can extend lateral movement to one side by attaching the gimbal/camera with one strap to one support arm only. It takes seconds to make the change, then change back.
Note: ProArms increase lateral movement on both sides, and even more to one side if only one arm is connected.