Does OSX Lion only support certian graphics cards, or processors?
Yes, but don't expect Apple to enumerate each one. You'd have to determine that on your own.
Moreover, would my previosly purchased Lion download, be legally applicable on my new computer.
This would be a violation of Apple's terms and conditions to which you agreed as a condition of purchasing Lion:
See paragraph 1.I: "Other Use Restrictions"
By "build" do you mean a PC hackintosh, or do you mean you have an old intel Mac and are going to re-assemble the insides from bits and pieces from other Macs? Apple system software is only licensed to be run on Apple hardware. If you are rebuilding a computer then I believe if you purchased an upgrade version of Lion (vs. had it come on another Mac you own whereby it is tied to that Mac) then you would be entitled to run it on a rebuilt Mac.