If your Wi-Fi card allows it, you can configure your Lakka box to behave as a local Wi-Fi access point.
In the cmdline, add localap to enable the service.
You can also enable it from SSH with:
systemctl enable localap
systemctl start localap
But before this, you will need to create a /storage/.cache/services/localap.conf containing the SSID and the password (8 characters min):
APNAME=LAKKA
PASSWORD=BLAHBLAH