That's a horrible budget if you want a laptop to actually play games and it be "playable". If you have such a small budget, just build a desktop. You can build a desktop the same price that will outperform any laptop. But even for a desktop that's pushing it.
A lot of people say "anything can play league" and those are the same players complaining that they freeze every team fight and then they make a board post blaming Riot like it's their fault your playing on a toaster. Like they really expected their wal-mart hello kitty pink Laptop to be able to run games....
Don't be that guy man plz xD
Just save up for a little while, put some cash aside from every check and save for a month or 2. Also, lots of pre-built options aswell, especially around any kind of holiday. Ibuypower is probably one of the best priced companies, but building it yourself will always be cheaper.