To repair permissions for Lion, is it safe to use Disk Utility in Recovery OS for Mountain Lion?
The diskutil repairpermissions /Volumes/whatever reads the BOM and receipts from /Volumes/whatever and not /. You can validate this with fs_usage and installing OS X on an external volume and running the check while snooping the IO.

It's always preferable to have the OS doing the repairing match the OS on the volume being repaired, but I've never been bitten with a problem by mixing things where a newer OS repairs an older OS. I've gone the other way in a pinch and not had it blow up, but I did make plans to run a proper repair when time was available soon thereafter.

Also - this is a very rare tool and like antiboitics, often gets prescribed erroneously. Repairing permissions only twiddles with Apple software and rarely is a problem due to incorrect permissions on a log file or an Application bundle.