Minimum System Requirements
2 GHz processor
1 GB RAM (Windows Vista and 7 users will want 2 GB of RAM or more)
8 GB available hard disk space
Shader version 2.0 capable video card
Support for DirectX v9.0c or better
Windows XP (Service Pack 2 or 3 ONLY), Windows Vista, or Windows 7
Recommended System Requirements
3 GHz processor
2 GB of RAM (Windows Vista and 7 users should use 4 GB of RAM or more.)
12 GB available hard disk space
GeForce 8800 or equivalent video card (Dedicated GPU with 512MB+ Video Memory(VRAM.
Support for DirectX v9.0c or better.
Windows XP with the latest service pack installed, Windows Vista with the latest service pack installed, or Windows 7
The latest update to.NET Framework from Microsoft
The latest version of Adobe Air is required to connect to PVP.net. Adobe Air is included with all League of Legends setup files, but can also be downloaded from Adobe's website.
I have not played League of Legends, but based on the specs recommended by the company, your PC should be able to handle it nicely.