Will this computer be able to run League of Legends with 40+ fps?

I'm going to go with Brett here.

http://www.notebookcheck.net/NVIDIA-GeForce-Go-6150.6945.0.html
I mean it benchmarks 6 fps with medium on a game that came out 5 years earlier.

But it does run DirectX9. So you could probably run LOL.
With the lowest settings maybe you'll get to 40 fps.
Not likely, but maybe.

From that page though:
•Also supports PCI Express x16 graphics cards*

So you could upgrade it, I suppose.