Lightning wouldn't have the same issue in that case because there's no transaction trace on Lightning, but there is on Monero. Gresham's law only applies in the context of a market that accepts both Monero and Bitcoin (or any other currency). If the option is there to pay in Bitcoin or Monero, most will choose Monero because it's worse to hold. If the only option is Monero, then that doesn't apply.

Lightning uses onion routing. Tor implemented onion routing, which Lightning copied. Try reading the Tor whitepaper, it's right there at the beginning what onion routing can't protect you against: a global passive adversary. A GPA has existed for many years. It's called the NSA. Onion routing doesn't provide you with the privacy and anonymity you think it does, sorry. (but it's better than nothing)