This is a how to install League Of Legends. Working on my Dell Precision M6700 running Ubuntu 17.04 as of 2017-06-07.

Install Lutris

From https://lutris.net/downloads/

ver=$(lsb_release -sr); if [ $ver != "16.10" -a $ver != "17.04" -a $ver != "16.04" ]; then ver=16.04; fi 
echo "deb http://download.opensuse.org/repositories/home:/strycore/xUbuntu_$ver/ ./" | sudo tee /etc/apt/sources.list.d/lutris.list
wget -q http://download.opensuse.org/repositories/home:/strycore/xUbuntu_$ver/Release.key -O- | sudo apt-key add -
sudo apt-get update
sudo apt-get install lutris -y

Install League Of Legends

From https://lutris.net/games/league-of-legends/

Allow Lutris software to take care of lutris: links.

Choose a path, and let it install. It'll install in the given dir a version of wine, download LoL installer, additional stuff like DirectX or OpenGL... and finish wish a prompt for menu or desktop link.

Doesn't work ?

Known issue : LoL requires (Microsoft) TrueType Fonts. Install those with

sudo apt install ttf-mscorefonts-installer

I'm 99% sure about this fix, for the missing 1% I did apt install -y wine-stable winetricks in search of a solution. An alternative might be to edit the install script and add a winetrick to install corefonts.

Otherwise launch lutris from a terminal with debug enabled to have a hint : lutris -d. You might find help on IRC, server freenode, channel #lutris.