As I already said the video and sound settings are set to maximum. These settings cause lag, so to get rid of it you can adjust the settings to the minimum, to get a lag free game. Just do this:
1. Start the game and open the options
2. (Optional)Open the Music and Sounds Menu and turn the sound and music off, this as well causes lag
3.Open video settings
4. Now lower the render distance as much as you want.
4a.Change the graphics to fast.
4b.Change the Max Framerate to Unlimited.

Custom resource packs can cause lag, the most often problem is the resolution. If you are using a resource pack that has a resolution of 128x128 you are going to get lag. So to fix this look if that texture pack that you are using is available in lower resolutions like 64x64 or 32x32 or 16x16. I'm sure that many of you are using a custom resource pack, but some of you maybe are still getting lag with the default resource pack as well, if you think there is no help for you than your wrong. You can download simple resource packs that reduce the lag and if you are still getting lag you can download super low resolution resource packs like 8x8 or 4x4 or 2x2 or even 1x1. These are going to make your game 100% faster, the only problem they are ugly but it still removes the lag.

There are some here on Planet Minecraft, feel free to search for some!

I'm sure many of you have heard of the popular minecraft mod called Optifine (www.optifine.net). This mod makes the game run faster, just download and install it.

You can find some tutorials on Youtube:
How to install optifine