Naruto might be very protective of Lily. He would use his skills to keep her safe from the walkers. Lily could be in awe of Naruto's powers at first. Then she might start to learn from him, like how to be more brave in the face of danger.
It could be really interesting. Naruto's ninja skills might come in handy in the zombie - filled world of The Walking Dead. Maybe he could use his shadow clone jutsu to distract the walkers while Lily and others find safety. He could also use his speed to quickly gather supplies. Lily, depending on which Lily we're talking about, might provide a more emotional and human side to the story, perhaps being the one to comfort those who have lost loved ones to the walkers.
Michonne does die in the comics. The circumstances surrounding her death were quite dramatic and had a significant impact on the story's progression. It happened during a major conflict with other characters.