My computer specifications:

• Intel Core i5-4570
• 16 GB Memory
• Radeon HD 5770

I followed the instructions here, with these changes:

• Using video driver “fglrx-updates” (the tutorial talks about NVIDIA cards)
• Did not install TuxLoL
• Did not do anything regarding the “Maestro error” since it only applies to Optimus Notebook users
• Did not follow step 6 because I did not run into the problem for big item icon text for the item shop
• EDIT: Thanks to Ingvar’s comment, the installation progress for the game can be viewed like so: open terminal (Ctrl+Alt+T) and execute:

tail -f ~/.PlayOnLinux/wineprefix/LeagueOfLegends/drive_c/Riot\ Games/League\ of\ Legends/Logs/Patcher\ Logs/*.log

There are also other steps that I had to do, which I read from here:

• Click configure for the “League of Legends” entry in “PlayOnLinux” and find the “Display” tab and then choose the following options:
  • Direct Draw Renderer – gdi
  • Video memory size – 4096 (or something else depending on graphics card)
  • Offscreen rendering mode – fbo\0
  • Everything else on default
• Create a file called “game.cfg” in the directory “/home/your-username-here/PlayOnLinux’s virtual drives/LeagueOfLegends/drive_c/Riot Games/League of Legends/Config”. Below is what I have in my “game.cfg”:

[General]
EnableAudio=1
GameMouseSpeed=10
UserSetResolution=1
BindSysKeys=0
SnapCameraOnRespawn=0
OSXMouseAcceleration=1
AutoAcquireTarget=0
EnableLightFx=0
WindowMode=0
ShowTurretRangeIndicators=0
PredictMovement=0
WaitForVerticalSync=0
Colors=32
Height=1080
Width=1920
SystemMouseSpeed=0
CfgVersion=5.3.296
x3d_platform=1

[HUD]
CameraLockMode=0
MiddleClickDragScrollEnabled=0
KeyboardScrollSpeed=0.5000
ChatScale=50
ObjectTooltips=0
AutoDisplayTarget=0
ShowAllChannelChat=1
ShowTimestamps=1
ItemShopPrevY=39
ItemShopPrevX=106
NameTagDisplay=1
ShowChampionIndicator=0
ShowSummonerNames=1
ScrollSmoothingEnabled=0
MiddleMouseScrollSpeed=0.5000
MapScrollSpeed=0.5000
ShowAttackRadius=0
NumericCooldownFormat=1
SmartCastOnKeyRelease=0
EnableLineMissileVis=0
FlipMiniMap=1
ItemShopResizeHeight=0
ItemShopResizeWidth=164
ItemShopPrevResizeHeight=1080
ItemShopPrevResizeWidth=1920
ItemShopItemDisplayMode=1
ItemShopStartPane=1

[Performance]
CharacterInking=1
ShadowsEnabled=1
EnableHUDAnimations=0
PerPixelPointLighting=0
EnableParticleOptimizations=0
BudgetOverdrawAverage=0
BudgetSkinnedVertexCount=0
BudgetSkinnedDrawCallCount=0
BudgetTextureUsage=0
BudgetVertexCount=0
BudgetTriangleCount=0
BudgetDrawCallCount=0
EnableGrassSwaying=0
EnableFXAA=0
AdvancedShader=0
FrameCapType=6
GammaEnabled=0
Full3DModeEnabled=0
AutoPerformanceSettings=0
CharacterQuality=4
EffectsQuality=4
EnvironmentQuality=4
ShadowQuality=4
GraphicsSlider=6
paths=0

[FloatingText]
EnemyTrueDamageCritical_Enabled=1
EnemyMagicalDamageCritical_Enabled=1
EnemyPhysicalDamageCritical_Enabled=1
TrueDamageCritical_Enabled=1
MagicalDamageCritical_Enabled=1
PhysicalDamageCritical_Enabled=1
Countdown_Enabled=0
EnemyTrueDamage_Enabled=0
EnemyMagicalDamage_Enabled=0
EnemyPhysicalDamage_Enabled=0
TrueDamage_Enabled=0
MagicalDamage_Enabled=0
PhysicalDamage_Enabled=0
Score_Enabled=0
QuestComplete_Enabled=0
QuestReceived_Enabled=0
Disable_Enabled=0
Level_Enabled=0
Dodge_Enabled=0
Heal_Enabled=0
Special_Enabled=0
Invulnerable_Enabled=0
Debug_Enabled=0
Absorbed_Enabled=0
OMW_Enabled=0
EnemyCritical_Enabled=0
MagicCritical_Enabled=0
Critical_Enabled=0

[Volume]
SfxVolume=0.5
MasterVolume=0.5