>>279702251 (OP)He could have won before Rem was introduced. All L had to do was ask his CIA buddies to abduct Light the minute he suspected Light of being Kira. Light was literally his only real suspect, so might as well just in case, and once the Kira killings stop without Light having had the chance to set up a second Kira, he'd be fucked. But L was too obsessed with "winning" in his own dumb detective way, he treated Kira as a puzzle to solve and not as a threat to eliminate no matter what it takes.
Light should have been doomed the moment he thought it was a good idea to intentionally allow L to know that Kira has access to police information, it made it inevitable that the suspect pool would narrow him down.