After way too much time spent on this, we found the problem is twofold. Hopefully this will help someone else in a similar situation.
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In the Lumens, to get it to recognize a new stream key for Facebook, we had to put in some random text characters in the stream key field, save the changes, paste the new stream key, and save the changes. That would generate the preview and allow streaming to Facebook no problem.
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We found there was a greater issue present. The internet speed at the building where the encoder sits was supposed to be 100 / 7, but they were not getting anything close to that. Once we got Facebook working in addition to YouTube, we found streaming both caused them to be extremely choppy.
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After having an ISP technician out to the building last week, they said the wiring in the box outside the building was awful, we were at the end of the line, and that he was surprised we ever got internet signal to the building. They are working on clearing up the pipe now so the signal is strong and clean, and we're upgrading to 200 / 10 pretty soon. We also changed the video resolution we're sending to YouTube and Facebook so we're using a lot less bandwidth to ensure we don't use the entire upload pipe.