I think I see the problem from your screenshot. Do you see that textarea above the keyboard? That's the preview area that shows what is going to be sent to the game (which is paused while the keyboard is on-screen) when you press the green check mark. When you press the green checkmark button then it is all sent (as if you typed it very very fast on your keyboard). Note that there are 2 different backspace keys on that keyboard. One is for sending backspace to the game (it will put [BACKSPACE] into the preview area) and the other will actually remove the keys from the preview area. (like you'd expect a backspace would)

I don't have LoL yet so here's what you should try (while you're in the middle of the game, not in the menus):

• Press F1 in the virtual keyboard and then submit it with nothing else in the preview area. This should do an attack I think.
• Press ESC in the virtual keyboard and then submit it. This should bring up the menu I think.

.

If you have an actual PC besides the tablet, you can play scummvm daily builds on it too (and even exchange saves between it and the tablet, they're compatible across platforms for the most part) This way you can test what keyboard keys work for LoL (sorry I am just guessing at this point based on what people tell me the keys are)

Have fun!