Hi,
This issue may be due to a possible hardware or software issue. In order to isolate the problem, let's go through several troubleshooting steps.
Let's first try to update your drivers to ensure that everything is working fine on your device. We recommend you run the Surface Diagnostic Toolkit (SDT) in order to be able to update all drivers for your device. To find out more, please click on this link.
SDT will be able to determine if there are any issues with any of your drivers. Try to see if the issue still persists after the update.
If the issue continues to persist, we would like to clarify on our end if the touch lag is with the screen. If it is with the screen, you may follow the advise of MVP Barb Bowman which can be accessed through this link.