Why don't you also tell us the laptop(s) you are thinking of buying, so we know what you have in mind. I doubt anyone here knows the specs for "most laptops" under $500.
Or you could use Google to look up the specs of whatever you are thinking of buying.
By the way, if you're thinking you are going to get decent performance out of Lightroom on a laptop that costs less than $500, well I don't think so. It might run, but I'd be skeptical that it would run well.
processor and graphics card are a little new to me.
As far as processor and graphics card - pretty much any new computer will run Lightroom, so you really don't have to worry about processor model (or display adapter specs), as far as compatibility is concerned.
Of course 4 cores is better than 2, and faster is better than slower, and more memory is better.. - but all new processors and graphics interfaces should run it (even if graphics interface is not on a "card").
One thing: 2GB is NOT enough ram to develop raw files. jpegs: maybe, raws: no.
For raw files, 4GB is a better "minimum" (3.5 if you MUST run 32-bit Windows ***, but don't do that if you can help it!), and for BIG raw files (megapixel-wise), you may need 6GB, minimum.
*** make sure the OS is 64-bits.
It also depends on the camera type and file format you will be using with LR. What camera model(s) and do you plan shooting raw file format (you should!). The higher the Megapixel the camera the more processing power you will need to keep LR operating smoothly.
I ran LR3.6 on a 3.0GHz Pentium 4 single-core system (XP, 32bit, 2GB memory) with no real issues when processing Canon 300D 6.2 Megapixel image. When I bought a Canon 5D MKII the 21 Megapixel raw files brought the system to its knees making it unusable.
You can compare relative processor performance at Passmark:
I can make specific recommendations once you tell us the camera models you plan using with LR. Please also include future camera models you plan on using with this laptop.