Yes Lexicons work the same for public & permissioned data.
I actually expect 3 layers (at least for the usecase of communities/groups): the protocol, a cross-app community governance/structure standard, and then application Lexicons.
We’re discussing what an atmospheric community is over here: What is an atmospheric group/community?
And I shared some early thoughts around some data modeling questions in this blog post: Modeling communities on permissioned data - Daniel's Leaflets