Well ok. Here are a few things I found out towards working on your solution.
restart layout was resetting everything based around session storage. However, it did not reset Webstorage Local(ie long term). You might be able to get away with other methods by using another layout that has some vars or something, but I wanted to minimize any tampering to your own work.
For now it uses local storage. Just remember when players do a fresh start to manually set the lives at the main menu before starting the game play.
Hope you find it of some use.
Thanks for the vote of confidence Space Ape, but I'm a noob at C2 :D. I just find the more I try to help the more I get my hands into quirks of C2 and become better at it over all :D