if it’s possible to connect to an iCube via my WiFi network and use Lightburn?

No, that’s not possible. It does not feature the required protocol, as far as I know. It’s just a simple web interface that is used over Wi-Fi. But to be honest, I didn’t investigate further yet.
In general, I highly recommend avoiding any wireless communication, it increases the risk of fires drastically.
If you still need wireless communication, switch to Bluetooth, this can be used with LightBurn.