Reinstalling Mac OSX Lion on Locked Disk

I have a 2011 vintage MacBook Pro which is not booting at all. It gets to the gray screen with Apple logo and does not move ahead from there. I pressed Command-R at bootup to enter the disk utility screen.

• I ran the disk check utility on the HDD and it returned OK for all checks.
• The verify/repair disk option for the boot drive was greyed out.

When I try to re-install MacOSX Lion by using the internet, it gets to a screen where both the disks to install MacOSX on are greyed out and there is an error message that says "This disk is locked". I went through this question that suggests re-formatting the hard drive to create a new partition and re-trying.

My questions:

• Are there any other options I can try without needing to reformat the hard drive?
• Is there a way to back up the hard drive before I try the above?
• In the Disk Utility section, the boot drive was greyed out disallowing any repair. Any reasons why?

If you have enabled FileVault once, the disk will be locked. Try open disk utility and mount it. It should ask for a disk password. Enter your disk encryption passwords which you entered when you setup FileVault. And, you're good to go.

If you forget disk passwords, you should try resetting with iCloud. Else, you'll need to format it.