Unresponsive screen

The iPhone 8 will support the latest iOS, 14.7.1. You should update, however if you are experiencing a problem with the screen, you may not be able to. See this first about the screen. If the screen isn’t working on your iPhone or iPad - Apple Support

If you have a computer, and have used the iPhone with the computer before and it is trusted, you can update via the computer. Update your iPhone, iPad, or iPod touch - Apple Support

The phone should not lag. Make sure you always keep at least 10% of the iPhone's total capacity free at all times for best operation. If the screen is doing this intermittently, then you may wish to set up a Genius Bar appointment at your nearest Apple Store for Apple to test the device. They will explain your options from there.