My computer works perfectly fine on my 32'' LG tv
I am also able to log on LoL client and do everything
But when I try to get in a game, my tv goes blackscreen and it says the resolution isnt supported.

Any thoughts ?

Navigate to....

C:\Riot Games\League of Legends\Config, open "config" with notepad. In the Width and Height field enter in your TV's resolution. Save it, launch a practice game to make sure it works. If your TV is 1080P it would be 1920x1080, so Width would be 1920 and Height would be 1080.

You're creating a game where the resolution you are putting to the TV is greater than what it can support. You need to figure out whether it's 720P or whatnot, so you can set your resolution on your computer appropriately.