Booting 10.7.5 Bup from 10.8.3 computer
 

Is it possible to boot an OSX 10.7.5 backup from a OSX 10.8.3 Computer?

Not if that computer doesn't support that version. Basically, if it shipped with a version after that, it's really unlikely.

Try it and see !!
 

Dave is probably right (he usually is!), but I'd give it a try anyway. I have a MacBook Pro, bought from Apple on Dec 1, 2011, that came with Lion pre-installed (I've since upgraded it to Mtn Lion).

The MacBook readily boots to a Snow Leopard backup made with SuperDuper! on another computer. It easily runs everything on the backup, including a few legacy apps I have that need Rosetta.

If, after the Snow Leopard desktop first comes up, you get a message saying "Where is System Events?", followed by a whole page of choices, just go to the bottom of the page and click on the "Cancel Button". (The first time this happened to me, I researched the issue and came to the conclusion that this would work for me, and it has. I don't remember the details.)

The "System Events" thing happens when the OS hasn't managed to rebuild its launch services database before something goes looking for a component (like System Events). Nothing to worry about.

But, while you can give the boot a try, like I said, it's pretty unlikely if the Mac shipped with 10.8.3.