Alt+Tab is usually supposed to work in Ubuntu for switching applications, even from a full-screen program. However, when you're running a Windows application with Wine, it does not always work. I don't have League of Legends, but the technique described in this post of this Ubuntu Forums thread may help.
Press the Super key (i.e., the Windows key) and type in: configure wine
An icon for Configure Wine should appear in the search results. Click on it. The "Wine configuration" window will come up. Click the "Graphics" tab.
Check the box that says Emulate a virtual desktop. Unless you want your game to appear in a Window that's smaller than the whole screen, you'll probably want to fill in your current resolution for Desktop size. For example, if your screen is "1808p", you'd replace 800x600 with 1920x1080.
This should make it possible for you to Alt+Tab out, because this makes Wine encapsulate your game in a window. Even if the game itself doesn't like to be minimized, and even if there is a bug in Ubuntu preventing it from being minimized, this should usually work around the problem.
It might not work, though. If it doesn't, I recommend trying other shortcuts, as Hugo Vieria suggested, and also the general, Wine-nonspecific method that Oli has suggested.
Finally, the Emulate a virtual desktop setting will affect other Windows programs you run with Wine (if any), but you can change it (and change it back) as needed.