The lock icon on the host/server PC will disappear from Moonlight, and you're free to use it from the client system.
Assuming your PC has enough horsepower, you can run two Sunshine server instances and stream them to two different Moonlight apps on your smartphone/laptop to simulate a multi-monitor setup.
According to a Reddit user who says they are a Product Developer for Razer PC Remote Play, the app is built on the open source Moonlight/Sunshine projects, with the goal of simplifying setup and ...