Will this computer run minecraft smoothly (no lag on max settings)?

No, the graphics card (820m) is too weak. It can run minecraft at low settings and short render distance but probably not with a smooth framerate (less than 30 fps). Search for YouTube videos for people playing minecraft with this graphics card and you will see.

If you want a better Minecraft experience find a computer with better graphics card (that's the most important part, it will be the bottleneck when it comes to Minecraft, and most other games too).