RXNFS
 
I have the same LZ CANBUS for my 07 Lexus GX 470 and I was having issues with it working correctly until I plugged in a 8 pin connector from the harness into the back of the DUDU7 head unit.
This is the connector from the harness, it is a 8 pin with I think 2 green wires coming from it.
and I plugged it in to the "Protocol Serial Use with Can-bus" port on the back of the DUDU7.

Once I did that, everything is now working great. Steering wheel control buttons all work properly. The HVAC buttons work perfectly and even the temperature display is showing the correct temperature in Fahrenheit. I used the same CANBUS settings that you have (LZ(HZ)/Toyota/LEXUS IS/NO AIR AMP.
You might already have that plugged in but if not that might be your problem as well.