I also think about having plausible deniability. Using lightning as it was intended is about the most normal thing you can do with bitcoin, and it offers moderate privacy. The problem is with all these LSPs moving in.  

 Lightning as it is right now is pretty private, but businesses will likely be told to run OFAC compliance nodes like this, at which point noncompliance comes in to play. 

https://www.nobsbitcoin.com/amboss-launches-reflex/ 

 I can imagine these businesses will want to keep it a secret if they are running this software which makes it hard to vote with your satoshi.