Yes, what you should have already: an alternate system boot drive.
Do an install on another drive. All you need is say 40GB is more than ample.
Just Mac Apple OS and any favorite tools you need to boot your system and run, not a full working OS with all the OS and stuff. THAT you can make by cloning this safe emergency boot system to another drive.
That way you have
a dead boot drive
a good emergency system for maintenance
a solid foundation for a system - and here you want about 200GB at most often much less for OS and apps.
You can then use your backup to import, migrate, and ONLY touch or import from the sick system drive essentail file that you did not backup or have elsewhere.
when a drive or system is sick the last thing you want to be doing is using it.
Clone
Disk utility has RESTORE which will also clone your system but not the Lion Recovery partition. Oddly Apple did not 'endorse' making bootable clone of the system which works too but most choose Carbon Copy Cloner - it works more consistently; it allows for smart update of the backup volume. Both can backup to a sparse disk image if desired.
Using Cloning as a Backup Strategy
http://www.bombich.com/software/updates/ccc-3.5.html
OS X Lion Install to Different Drive
How to create an OS X Lion installation disc MacFixIt
Migration Assistant Update for Mac OS X Snow Leopard
http://www.apple.com/support/lion/installrecovery/
Create an OS X Lion Install disc
http://reviews.cnet.com/8301-13727_7-20080989-263/how-to-create-an-os-x-lion-ins tallation-disc
How to clone your system:
http://macperformanceguide.com/Mac-HowToClone-backup.html
http://macperformanceguide.com/Mac-HowToClone.html
http://www.macupdate.com/app/mac/7032/carbon-copy-cloner
http://www.macperformanceguide.com/blog/2012/20120711_2-MacPro-internal-clone-ba ckup.html
You may of course need to pick up some new system and data drive to work with.
$100 buys: 1TB WD Black / 128GB SSD also a worthy system drive / 250GB WD 10K VelociRaptor are nice too.
Isolate the system and all your data and media files and have them on separate disk drives makes life easier - onlythe core /Users/KL_home_account_folder/Library
is needed on the system drive (makes life easy) and keep all the data safe and on separate disk drive - like WD Black 1 or 2TB for instance.
Use emergency system for maintenance
Also always clone your system to another drive before making changes or updates, that way you know yhou have a safe good bootable system - and in a pinch, you can reformat/erase and restore (system does not need to be backed up except for home email and such and CCC or Superduper can do that in under 10 minutes).
Fixing a sick drive when it FIRST happened can be done, but then it is like an onion or tangle of string that can't be pulled straight. The disk directory may not be easy and the journal can't fix.
There are 3rd party tools that can or have good chance but then the one I would use and recommend is $90, better to put that into a new drive unless you already have Alsoft Disk Warrior.