The Mega, which uses the most powerful chip of all the Arduino models, has 8kB of RAM. A single frame on a 640x480 8-bit color display is 300kB. You're going to need something more powerful than an Arduino.
If you insist on trying with an Arduino (it's not completely impossible, it'll just be really slow and complicated) you'll have to look around for the pinout of the specific LCD you're using - they're all different. Alternatively, you could leave the LCD attached to the laptop and have the Arduino send the numbers to display to a program running on the laptop. (Computers already have the special electronics needed to drive displays, it's usually known as a "video card". You'd essentially wind up building your own video card any other way.)