Log into the main LnL web site (not the forums), go to My Account, and there is a tab for Serial Keys. It should show you existing keys and give you Steam keys for CO2 and each DLC you own.
Download the game engine for free on Steam, and on Steam you can then add Steam keys for all the DLC you own. (I don't remember the exact process to do that but I do remember it was easy to figure out). Then just start the game with the "Play" button on Steam and away you go. When they release a new update, the Play button will say Update.
Dave