Turn off firmware lock with OSX 10.6 which has no recovery mode

You need to be using the correct 10.6 DVD for that Mac assuming OS X 10.6 is compatible with it. There is a Restore DVD (gray DVD label made for one specific Mac) and an upgrade DVD for Macs which were able to run 10.5.

If you can boot this Mac using an external drive, then you can create a bootable macOS USB installer using the instructions in this Apple article:

Create a bootable installer for macOS - Apple Support

For a 2011 Mac, I recommend macOS 10.13, but if macOS 10.6 is the only OS ever used on this Mac, then it would be best to go with macOS 10.11 first. I would recommend installing macOS 10.11 first so that the system firmware is updated because that may be required before using/installing macOS 10.13.

You can still create & use a bootable macOS installer to achieve your goals. Either the macOS 10.11 USB installer has an option to access the firmware utility to disable the firmware password lock, or you can install macOS 10.11 to an external USB drive & upgrade the external USB drive to macOS 10.13 High Sierra. Once you do this, then the laptop will have access to Internet Recovery Mode which definitely will give you access to the utility to disable the firmware password lock. All without affecting your macOS 10.6 installation on the internal drive.

However, you should definitely have a good backup just to be safe....you should always have frequent & regular backups anyway.

FYI, the current macOS 10.7 Lion installer is not the same as the older versions, so I'm not certain it will be easy or even possible to make a bootable USB installer from it. You are better off creating a 10.11 El Capitan bootable USB installer instead since Apple has very clear & easy to follow instructions for doing so. Same with macOS 10.13, but like I said, I'm not sure if 10.13 can be used if macOS 10.11 was never previously installed.