Lock/unlock behavior differs from vanilla
Tested vanilla behavior in latest official GOTY version from Steam, running only Morrowind.esm with Tribunal and Bloodmoon. No other plugins or utilities used. In vanilla, organic containers (such as fauna, egg sacks, ore veins, Fargoth's hollowed tree stump, and even mage/fighter's guild supply chests) can't be locked by Lock spells. Whether it's on touch or target, from a spell or magic item, the Lock spell effect just doesn't seem to lock organic containers.
Tested OpenMW behavior in 0.45.0 and in the nightly build. In OpenMW, you can cast Lock spells on organic containers, and they behave just as any normal container you lock. You can cast Fenrick's Door Jam on a mushroom container and then use Ondusi's Open Door or a lockpick or whatever you want to unlock it.
Note: While you can't use magic to lock organic containers in vanilla, you can use the console. Open the console, select the container, type "lock 50" or whatever value you want, and it locks. Organic containers locked like this in vanilla can be lockpicked, but open spells will not work on them like they do in OpenMW.