I use SNAPSHOT firmware zyxel_keenetic-extra-ii-squashfs-factory.bin on my Keenetic Lite III. Its work, but not LEDs and WiFi down time to time. After installation SNAPSHOT i can connect to device from LAN/Wifi (default OpenWrt network) by ssh.
IN any case, since I do not see your device officially supported by OpenWrt: Where did you get the information from that an OpenWrt image for the Extra II will work on your device?
Yes. Lite III is not ofical support, but HW is same as Extra II and i experementally try use FW from Extra II on Lire III Rev B and it worked for me, but SNAPSHOT FW only. RELEASE firmware dont work :))