Thanks for reading my question. I’ll try to be brief, yet descriptive and I appreciate your time in advance with any help!
Any ideas or suggestions on how to accomplish this?
Lightroom cannot deal with green screen compositing. You need Photoshop for that. Unfortunately, outside of Lightroom, there is no Adobe product that can watch a folder as far as I know. All Lightroom can do with a watched folder is to automatically import the files, nothing else. It is possible to script Photoshop from outside using tools like Apple's automator or a shell script combined with Photoshop droplets or batch actions which could indeed watch a folder and do everything you are describing, but this is quite advanced and will take quite some programming. Simplest might be a droplet that you simply drag files on or use an external batch utility to run on your images.