It does matter. The trace started by sending money to the perp and waiting for him to send it to an exchange, who they then contacted. They needed to see the transaction on the blockchain to know who to call. With lightning, they can't do that. They can't do step 2 -- the step where they watched the blockchain to see when the money moved, alerting them to check if it was sent to an exchange, who they could then get info from to find out whose account it entered. They wouldn't know it ever moved, or where, so they wouldn't know to call someone, or who to call.
Discussion
"Hey, people were colluding with, let us know if any of these IP addresses interact with you"
???
Not rocket science...
In the finnish example they didn't know his ip address at the beginning. The only thing they could do was send money to him using his DNM website and then wait for him to do something with it. They did that, and when he sent the monero to an exchange, they recognized the address, contacted the exchange, asked them what account he sent the money into, got the KYC info for that account, and went to his house to arrest him.
That is an example of a situation that lightning fixes: they can send him money but they can't see when it moves next. So they don't know he sent it to an exchange, don't get to read the exchange's address off the blockchain, don't know to call them, and don't learn his KYC info.