Why lithium peroxide? Why not any other alkali or earth-alkali peroxide? They would all work similarly, and be similarly useless.  First you would have to get your metal (energetically an expensive process) then you would have to form its peroxide (creating severe complications with your oxygen economy; the stuff isn't free, you know! It took a lot of phosynthesis to make it, including from trees!) Then you would combine it with carbon dioxide plus water, making a lot of nasty, soapy carbonate or bicarb, and then you would have to sequester that stuff where it could not escape, or you would have it all to do over, spending huge amounts of energy in each cycle.

Trees (and other photosynthesisers, whether biological or technologically synthetic) supply that energy from ambient light, preferably from sunlight. Instead of leaving us with waste to sequester, they leave us with materials such as wood, fruit, and tsunami-moderating mangrove swamps, that we can elect to use or conserve as we see fit. We are more likely to harvest energy from our in vestment in them than expend it, which is wht we should have to do with the metal peroxides.

Right?

Jon