QingPing Air Monitor Lite: Boost Your Health and Productivity 

I apologize for the late reply: things were a bit hectic with the New Year's celebrations and all. Qingping Air Monitor Lite does work in LAN mode without internet, at least via their own app. Even though you might occasionally see internet connection error messages, all the parameter values update normally. However, I can't guarantee for sure if this LAN functionality extends to the non-modified Mi Home app/Apple HomeKit. Although, you can definitely access the device's readings locally through other solutions like Home Assistant Integrations available at GitHub.