Yes the trail breaks when you transfer Munn to Speed via LN because it's happening offline and only who control the entry as well as exit nodes can link that if they want to and it is almost impossible via chain analysis to link back the transfer with KYCed address unless you reuse the address again to link with any KYCed funds again.
No, this is not true. The link is not broken and there are many ways you can be tracked. Please don't give incorrect information here.
But my question was mostly just technical - to better understand these things. So far I haven't parted with a single SAT yet. I don't trade or anything like that.
@Satofan44, thanks for the extensive reply. Much appreciated!!
I hope that you have understood that my answer applies pretty much directly to LN as well. Just think about it, starting with the address example. Replace XMR with Lightning and you get the same result. If you have any questions about any other points, but more specific to LN. Generally you can think about it this way: Almost everything is possible, it just depends on who is looking, how hard and how many resources are they willing to spend to track you?