Aperture can't be installed on Macintosh HD because Mac OS X version 10.7.5 or later is required. How do I go about that?

CALL (by telephone) the Apple online store in your country and they will sell you a download code for 10.7.5 and provide instructions. It is "put away" to keep people from buying less than the most recent version of Mac OS X by accident.

You will download and install it from the Mac App store, using the App Store Application built into 10.6.8 and later. If you want to save an Installable copy for later use, you must interrupt the process AFTER the download is complete and BEFORE the Installation is well under way, as the Installer image is consumed as it is Installed. Search for Lion Disc Maker for instructions.