Many .177 Lightnings seem to run at 10-11ftlb so some might just about stay below 12ftlb with a .22 barrel.

If the larger calibre barrel were slightly shortened it would allow both barrels to shoot at the same muzzle energy - I proved this with a TXHC which was originally .177cal with standard 9.5" Walther barrel and is now .25cal with custom 6.5" .25cal Walther barrel shooting with the same internals and at the same 11ftlb muzzle energy as it did when it was .177.

In some cases (not the Lightning) changing barrel length or calibre doesn't always have the expected effect; it depends on whether the barrel was longer than necessary to start with.