Can this laptop run next gen game on medium or low settings?

Lenovo Essential G505s
you can check the specs here: 'http://www.pcworld.com/product/1264562/lenovo-essential-g505s-notebook.html' ( or any other site you like ). Can this laptop atleast run assassins creed iv black flag with decent framerates.

No, the 2GB card is semi-ok, but DDR3 isn't good, and AMD mobile processors can't be that good either, so just buy a good (maybe even Alienware laptop) desktop, and have a good GPU (AC4 will at leas require a 2GB GDDR5 card to run decent on medium, and if you want high/ultra: AC4 lags on: 3x 2GB GTX 680, i7-3970X @4.5 GHz and 64GB RAM)

No. It will run it, but run it poorly. Please do not buy a laptop for gaming.