Can BetterDisplay save or lock Universal Control device positions?

No. BetterDisplay does not manage the positions of devices connected through Universal Control’s Link Keyboard and Mouse feature. Its display-layout protection does not save or restore those remote-device relationships, and it does not replace Universal Control’s connection handling.

Arrange those devices in System Settings > Displays > Arrange on your Mac. Drag the other Mac or iPad to the position you want relative to your displays. For intermittent connections, use Apple’s Universal Control setup and troubleshooting guidance.

Universal Control lets each device keep running its own apps while sharing keyboard and pointer input. Sidecar instead makes an iPad a display for the Mac. BetterDisplay’s Sidecar and ordinary display-arrangement features do not imply Universal Control support.