The nVidia drivers do not work on Asus laptops on default. IF you read the fine print on the nVidia website, they will say that the "your laptop" has a mandatory policy on driver downloads, only allowing them to be done so from the Manufacturer's website. The only way to circumvent this can be seen in older threads in the forum. I am not keen on providing you the link here, as I do not personally recommend the general user, or any Joe who stumbles upon this thread to do the procedures as they will have a hard time troubleshooting problems. However I can give you a rough idea on what it does. What happens when you install a driver through "THE" method is, the ASUS INI file that prevents you to install an nvidia driver will be overwritten by an nVidia one, which will allow future use of nVidia released drivers. Another method is to install beta drivers which by default do not usually have hardware checks. Again, I personally do not recommend doing these installations if you do not know what you are doing as you will not be capable of troubleshooting your own problems. Therefore, I recommend sticking with the drivers you have installed right now and find the source of the lag spike before adding another variable and/or problems.
Have you tried checking the temperatures? Can you provide more specifics on when, where and how often this is happening? What is your "other laptop"? What settings are you running at? Without a more detailed explanation, none of us are able to help, as we are just about as lost, if not more so than you are.
If you are truly keen on doing the installations, proceed to reading older threads, where you may also encounter the solution to your issues. Keep in mind, some functions will not be available, or may not work properly with the nVidia drivers, such as Splendid and/or screen brightness.