I think lobby needs on server saved autox layout selection. Same style than now in single player...

select layout on server you want to save to it, write /axsave layoutname

if you want to load a layout saved to server use /axload layoutname

and there is also /axlist to see list of layouts for chosen combo that have been saved to server

Just one thing to add, it may not be obvious for some. Once you save the layout (even on a public server), the actual layout file is stored on your PC and you need to upload this file to your LFS server, in order to be able to see it with /axlist command.

Example in picture.
Your track menu can load automatically on server saved layout, like than singleplayer.