Macbook Pro extremely slow when using video chat
It is more than likely that the increased demand on the GPU (processing and RAM) by supporting both the external monitor and the MacBook Pro screen while using Skype or Zoom causes the MacBook Pro to lag. Since you mention that the GPU is rather old and has only 1 GB of RAM, this is probably the problem.

Skype may give you the ability to lower the video quality and resolution, putting less demand on the GPU. If you can still Skype with the external monitor disconnected, this may be the best solution.