Why it is lagging

There could be a variety of reasons why it's lagging but most likely do to the game you're playing. If it's a graphic and memory intensive game it is most likely the reason the game lags... The model phone you have is more appropriate for basic games rather than memory intensive games.

The amount of applications you have installed or running in the background can also have an impact. Many scenarios can explain the lag and the touch screen freezing so try eliminating some of the strain on the processor when playing the game by closing unnecessary background tasks etc...