There is also a lot of UX issues and complexity involved in using LN privately and sovereignly that Monero (or even Bitcoin), don't have. Just a few:

-need capacity to use
-can't send larger amounts
-can't send to a static address
-can't use offline
-can be rugged if offline
-can ultimately be force closed back on chain against your will

I suspect, along with all the privacy holes, these are major reasons DNMs don't use LN and still wouldn't even if it's privacy was on par with Monero. Just too many inconveniences and pitfalls. A headache.