Keep in mind that even that is private, having so many back and forth payments, especially through few LSP, it could also trigger some "patterns". Not all LSP or routing nodes are "good guys".... choose wisely and learn better how to use LN with public and private nodes.

LOL maybe I should write a detailed guide about this. I wrote some in the past, but I do not like to give too many details in public about these aspects. I just want to show people the path. People still underestimate the power of LN... You have so many options and tools nowadays. Just using a single damn LN wallet is stupid.