I guess that's what we're about to find out. He allegedly stole 14 btc, worth over a million dollars. If he successfully obfuscates his trail via ln it will be a big validator of the privacy claims of its champions. If the tracers win, lightning devs can learn what to improve. There are about six or so cases where monero has been traced and additional charges were placed against criminals as a result:

Monero leaks

Perhaps this will be the first case where a lightning criminal is traced and caught. Or perhaps not. Time will tell!