I think it comes down to RP and using the proper communication channels so things aren't too confusing. etc.
If you want a Lords only senate message group then create a guild called "Senate of Fronen" in the capital city and get the lords to join it. If you're talking roleplay considerations then surely having a dedicated senate "building" in your capital is even more appropriate than a message group anyway?
But again, in my experience, locking regular knights and nobles out of important realm discussions is a great way to bore them and make them apathetic to the realm.
You can also create lords only referendums if you want to vote on something, or have votes cast publicly within your guild.
