You're intermixing two completely different sensors. You're thinking of the display panel that refreshes at 60Hz, all iOS devices had 60Hz, there has never been a 30Hz panel before until now with iPad Pro in order to save energy for when you're reading and don't need the speed. This has nothing to do with touch input.
The one you meant to talk about is the touch input sampling sensor, which operates on top of the panel. iPad Air 2 had a 120Hz touch sampling sensor and iPad Pro now has 240Hz. Before iPad Air 2, they all had 60hz sampling rate sensors. The reason the touch input lags a bit behind was because at 60Hz rate between the display panel and the touch sensor, there is not enough data to catch up in real time. With 240Hz, it is faster than the display panel, giving Apple enough time to predict the movement of the next input before the next refresh, making it smoother and doesn't lag as much.
You can learn more about this from Apple's WWDC 2015 session entitled: Advanced Touch Input on iOS.