Like Pi R already said, you don't want to get LiFePO batteries, that's lithium polymer (IIRC), and while they can provide much larger discharge, they have far smaller capacities.
You need to search for "16340" batteries, those are exactly the same size, but Lithium Ion chemistry. This is what we normally use in our lasers.
Aside from that, it looks it's fine.
Your build will consist of taking the C6 host apart, removing the empty pill inside and installing the pill with the driver inside (second-last item on the list).
Then you need to setup your module and heatsink, solder the diode leads to the leads coming out of the driver, and finally assembling the head.
Insert batteries and lase 520nm.
Out of curiosity, why did you choose 80mW 520nm as your starter build? It's a relatively expensive diode, when 200mW red and 150mW bluray diodes can be found for $6-7 each.