FWIW, this is what I used 8 years ago.
https://www.amazon.com/gp/prod...le?ie=UTF8&psc=1
When I was researching this, the biggest issue to consider is to ensure that the lens system you use stays on the phone (avoid the clip ons). That's the main reason why I went with a phone case system that will ensure that the lens stays in the correct spot. I used this for 2 years before I gave up on using my phone to stream as (1) my phone keeps overheating when streaming continuously under the sun; and (2) I realize that high quality video recording is more valuable/useful to me than streaming it. At that time, my phone can't stream and store HD video in memory at the same time. I went to a gopro connected to a mobile streaming device option that uses my phone as a hotspot. That worked fine in terms of streaming and storing HD video at the same time. But then I hit data limit issues. So now, I just focus on taking HD video and storing it, and I don't live stream anymore.