My experience with Lenovo laptops has not been good, to say the least. And this I am saying after being the owner of two different models of Lenovo laptops - the ideapad Y550 and the Z560. The Y550 was billed as a gaming laptop and TBH, I was quite satisfied with its performance back in the day. However, its processor gave up as soon as the warranty ran out and all I was left with was a very expensive paper weight. The Z560 was no different, though it was never meant for gaming, I do remember playing games like CODMW & Skyrim V on it, but soon started developing problems, especially with the keyboard, and that too after multiple replacement. I am still using the Z560 occassionally, with a few handicaps and only for basic day to day mobile computing. Lenovo service sucks - but that might not be the case all over. Anyways I will never suggest anyone to go for Lenovo laptops after what I have been through.
IMO - if gaming is your objective, build a pc yourself. I am pretty sure you would be able to get a pretty decent build within your budget and the experience in itself will be something to cherish for.