LAN Function (manage Yeelight bulbs locally)

I’m looking to handle all my smart devices (if not, then most), locally, without the need to go to the cloud/server, and the come back to my network, and be executed.

I know Smartthings is going this way (I have some devices that through firmware updates, are going to locale management).

Anyways, one of the reasons I bought my Yeelight bulbs, was it’s compatibility with all of my used systems: Smartthings, Alexa and Google Home, since I like to be as agnostic as possible in my smart home related stuff.

I was wondering, if the option of “LAN Control” in the Menu, is for this? Will this be managed locally in Smarthhings only? Alexa only? Google Home only? Inside the Yeelight app only? Thorough all of them?

I tried to read the manual, but it’s not so clear what this function does.

If NOT, is there a way to control locally, through any of the compatible systems?

Turning on the option “LAN Control” is the prerequisites for local controling of SmartThing and Google control.

And after turning ON this option, what should be the steps in Smartthings and Google Home?

Or does it happen automatically?