Lightning would help a lot.
For one thing, the most popular monero wallets (Cake wallet, moneroj) don't send transactions to their peers, instead they connect to a random node from a list of RPC servers and send it in plaintext to them. Lightning wallets, by contrast, (1) encrypt your transactions and (2) only send the encrypted blob to a single node whom you have a channel with. That's way, way better.
For another thing, monero wallets reveal the recipient's address to the sender. They automatically log that information and if the sender is an exchange or other public entity, they can be subpoena'd and begin tracing the payment. Lightning wallets, by contrast, do not reveal the recipient's address to the sender -- not the channel, not the htlc, not anything that actually holds the money. They only get to see a public key that is used strictly for communication, and thanks to trampoline routing, it is quite common for that pubkey to not even belong to the recipient. That's way, way better.
For another thing, monero wallets list all possible senders in every transaction (unencrypted btw) and put that information on a permanent ledger. Lightning doesn't do that. So if a person is being targeted and uses monero to send their money to a centralized exchange, the exchange's address will show up in that transaction and -- if the exchange discloses their addresses to the police, as many do -- the police can subpoena them for information about what transactions sent them money. They can then show them a list where the target's address shows up as a possible sender in each transaction, which is very good evidence that he sent the money. The target can be caught that way, as happened in this finnish case: https://cointelegraph.com/news/finnish-authorities-traced-monero-vastaamo-hack
Since lightning wallets actually encrypt the sender and do not even share the encrypted blob with the recipient, it would help a lot if the guy chose lightning instead. The police would not see a transaction going to the exchange on the blockchain, would not know to contact them and ask them for more info, and even if they did, the exchange would not have any info to link the sender's wallet to any particular account. That's way, way better.
