Time Machine, you will still need to put a working copy of OS X onto the new hard drive before you can access it.

The logical way to do this would be to install OS X from the 10.7 installation file, you do still have that file?, and then restore from Time Machine.

Not sure that Time Machine will take your machine from 10.6 to 10.8 but, because this is a fresh install, it is certainly worth a try.