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My iPhone 6 screen suddenly lag and becomes touch unresponsive . I need to push the power button to turn it off and on before It responds in my touch again . Do I need to replace my screen , or It just need a software update?

This probably doesn’t have anything to do with your screen. It’s your internal hardware. If it is still a fully original phone, you need to realize it’s +5 years old. Parts wear and can break down after a long while. Make sure your phone’s storage is not completely full, as this can slow down your phone. If this doesn’t work, try software-update (you actually need to do these always, anyways :D). If it still doesn’t work, make a back-up, reset the phone, and put the back-up back on there.

You may have to replace the digitizer/lcd assembly. Here is a guide