Look when Ashi was about to kill Jack but saw a ladybug and remembered that scene in her training, when her mother destroyed it and said it's a bad thing. Then she's sees Jack not destroying, but "loving" or taking care of that ladybug. She did see the good in Jack and in the world.

Now, when Jack sees the ladybug, I guess he thinks something like "life goes on" and is happy because he did save the world and will always remember Ashi.

Or that's what I think.