The fact that the LoL launcher doesn't offer a full screen mode is foreseeable, since it's a desktop application, like word etc.
It's more of a problem that it doesn't even offer window maximization.
To solve this, I would recommend writing a startup script using wmctrl.
wine lollauncher.exe & #the ampersand sends applications to the background
sleep 2 #wait for a few seconds for the window to actually spawn.
wmctrl -r PVP.net -b add,fullscreen
fg #only used to get the wine command back to the foreground
Please note that you may need to modify the window identifier passed to
-r as well as the wine command.
This is more of a workaround than a solution, but I hope it helps.
A clear problem with this is that it depends on the window to actually spawn after the specified amount of seconds. This could be messed up by things like the startup window etc.
A workaround for that (yay, I'm stacking workarounds today) would be to spawn a process in the background that periodically checks if a window named PVP.net is not in fullscreen mode and then adds the needed properties. If you need a script for that, I can whip it up too.