Watch Mac's iSight (webcam) on another Mac over LAN
Try IP Cam by Senstic available on the Mac App Store (no affiliation with the developer).

This app claims to work over a private network without needing active connection to the Internet. From the app description:


  INSTRUCTIONS:
  
  
  Start IP Cam on your mac.
  Take a note on the HTTP access address shown by IP Cam.
  For Wi-Fi remote viewing, enter the same HTTP address into the web browser from another computer or iOS device on the same Wi-Fi network.