What Computer Specs Are Needed to Run Minecraft Without Lag?

Intel Core 2 Qadro
Nvidia GT650
IMPORTANT: 4GB ram and more
64-bit operating system
Performance of games doesn't depend on internet connection
No more depending on performance of minecraft

Minimum Requirements:
CPU: Intel P4 or its AMD Equivalent (AMD K7)
RAM: 2GB
GPU: Intel GMA 950 or AMD Equivalent with OpenGL 2.1 Support
HDD: At least 100MB for Game Core and Sound Files

Recommended Requirements:
CPU: Intel Pentium D or AMD Athlon 64 (K8) 2.6 GHz
RAM: 4GB
GPU: GeForce 6xxx or ATI Radeon 9xxx and up with OpenGL 2.1 Support (Excluding Integrated Chipsets)
HDD: 150MB

I wouldnt worry much if your trying to see whether your computer can run it, try it, and if its laggy you can adjust all the settings to make it better.