Ok, lag is caused by your computer it is
Slightly minecraft's fault because the game can currently only us one computer core. Which most computers only have one but for example dual-core and quad-core will not be able to use the maximum possessing power, the game's lag can be solved 3 ways:
-Add another RAM card to your computer (
Newegg.comsells them) that will help
-Build a new computer (i built a computer for less than 250$ and it does very well)
-(the obvious thing you probably ignored) turn down render distance, change graphics to fast, install Optifine, turn off clouds, minimal particles, no smooth lighting. That is the free way to make minecraft faster.