yes. they are all talk they'll always say they can trace
Discussion
Chainalysis is pretty sus overall but it seems that, with enough resources, any digital currency will have some kind of privacy vulnerability. Just have to consider the tradeoffs.
There is no public data about lightning transactions. They can insert nodes in the network, but the data will be like those dandilion ip traces.
The fees are whatever their nodes ask for, not what the sender chooses.
The amount is slightly obfuscated in that there will be fees to account for, but that's probably the most revealing thing they can learn about.
If they are exit nodes, the fees might help them identify that, but not sure how they identify that they are entry nodes.
After all that, there is very little they can ask an exchange for when they want more info about a payment UNLESS the payment originated from that exchange. But a payment to an exchange is practically a blind payment for them.