When trying to edit a protected page in the Module namespace, Lua debugging console is not shown, even though it could be useful to test the protected module. See e.g. en:Module:Arguments (when not logged in as an enwiki admin, obviously.
There is a trivial workaround of editing any other (even nonexisting) page in the module namespace and starting the console session with some local m = require("Module:TheProtectedModule"), but why not make it easier?