The games gamemode doesn't change when opening to LAN. You can change the commands from OFF to ON, but not the other way around.

Expected behavior:

When opening a game to LAN, then updating the gamemode from survival to creative and the commands from OFF to ON, will update the gamemode and the commands.

Observed behavior:

When opening a game to LAN, then updating the gamemode from survival to creative and the commands from OFF to ON, the gamemode will stay in survival, but the commands will go from OFF to ON.

Steps to reproduce:

Gamemode

1. Start a world and choose a gamemode
2. Your world will now have those settings.
3. Go to 'Game menu' and click 'Open to LAN'
4. Now change 'Game Mode:' to something else
5. Now click 'Start LAN World'
6. Your gamemode has not been updated

Commands ON/OFF

1. Start another world and set the cheats to ON/OFF
2. Your world will now have those settings.
3. Go to 'Game menu' and click 'Open to LAN'
4. Now change 'Allow  Commands:' from  ON to OFF or from OFF to ON
5. Now click 'Start LAN World'
6. If you changed the commands from ON to OFF, it will not have been updated
7. If you changed the commands from OFF to ON, it will have been updated

I don't know how this is intended but it is not consistent.

Because many people use this to turn their commands ON in a singleplayer world and this is also used to set the settings for other players, I would suggest 2 different options when opening to LAN:

1. Set the settings for the host
2. Set the settings for the other players

Note:

This is all from the perspective of the host, I don't know how it affects other players joining.