I've never used a wireless keyboard before and am thinking of buying an entry level kb+mouse combo like the Logitech MK270r (just an example). I vaguely recall reading about lags with some wireless keyboards but cannot find anything about it with a quick search now. Is it still a characteristic of some inexpensive wireless keyboards?
I've had an experience of lags with an entry level keyboard and mouse combo from Logitech, the MK260. The issue was the battery used and the placement of the wireless dongle. Make sure it's as close as possible to the keyboard and mouse's line of sight.
Outside of that, if there's still lag and you're sure there's no issue with the OS and the drivers on your platform, you might want to return the keyboard and maybe add some more(due to store credit) and look into a more robust wireless keyboard + mouse combo.