Siri will need internet, but if you have wifi locally you can control them via a phone.
There’s also always the wall switch.
Telling Alexa to turn the lights on is more of a Rube Goldberg hack.
My system "relies" on an internet connection for just one thing right now: iPhone push notifications, which are merely informational and mostly for debugging. It also uses the internet to keep my local NTP server in sync. When I'm away from home I can manually check on stuff with a VPN.
In future I plan to expose a minimalist HTTPS api for triggering certain actions remotely, like the garage door. But even that's not a big deal right now because I've got a outdoor AP that covers a wide area outside my house—my phone is generally already on wifi as I approach home by foot.
An offline capable home automation system (including voice recognition) that can be managed by a non-technical person has a huge ongoing cost just in terms of keeping it working as it is, and that is before you change anything (if you can).
And somehow it manages to do this without running TCP/IP stack. I'm working on a project in the IoT space right now, and a Clapper is making me feel kind of silly about it.