Magic Keyboard Lag

Keyboard - Full Size Magic Keyboard, Space Grey...

I've noticed that when using the keyboard there's some sort of lag when tryping, but as soon as I connect the USB to Lightning cable all seems to be working without the lag. Ever since this has been happening, I also noticed that my Keyboards's bettery doesn't last - about a week to two weeks.

The question would be if this can be the keyboard battery?? If so, is it possible to replace the battery or does this mean I do not have a bluetooth/wireless keyboard anymore?

Looking forward to suggestions or feedback.

Thanks a mil...