How do I install new Mac OS onto a new unformatted HD The HD crashed on my old MacBook (white Mid 2007) and appears to be unrecoverable.   Though I bought a new MacBook Pro, I would like to resurrect my old MacBook, by buying a new hard drive.  (It had an 80 GB drive, and those appear to be really inexpensive).  

1)  Is there a way for me to get an OS onto my MacBook after I install the new HD?  (Can I do this myself?)  I think it had the Mac OS X Lion.

2)  I think that Apple keeps a record of my devices, and their OS's. If I went to the Apple Genius Bar, would they replace my OS for free and install it for me?
The MacBook 13" Mid 2007 is obsolete!  Meaning that even with the latest version of Mac OS X it supports, 10.7.5, the OS is no longer supported in any respect, has un-patched security flaws that will never be fixed. From a security standpoint, you'd be better off running a current version of Linux Mint then Mac OS X Lion 10.7.5 on that MacBook.

That said, if you really want to run the latest Mac OS X that MacBook model supports, then you'll need to acquire a copy of the Install Mac OS X Lion.app application bundle and use DiskMaker X (formerly Lion DiskMaker) to create the USB Installer as it does not support the createinstallmedia command found in the application bundles of the OS X installers starting with OS X Mavericks and later.

If you previously purchased Mac OS X Lion, then I believe it should appear under Purchased in the App Store and can be downloaded again and if not then you'll have to ask a friend to see if it's in theirs. 

Another possible option is to take the MacBook to an Apple Store and see if the Genius Bar can install a copy of Mac OS X Lion for you.