What are possible reasons for external keyboard input lag?
The lagging sounds like wireless interference to me.

Many devices can be the culprit; wireless routers, displays, other Bluetooth and WiFi enabled devices, and even devices attached via USB 3.0 cables with poor shielding.

The closer you can get your USB dongle to the keyboard, and the further it can be from sources of interference, the better. A good USB extension cable might be what you need to take care of this issue.