I have been advised not to use pressure treated lumber to build raised beds, but I just read your idea of lining them with pool plastic. If you did that, could you then use pressure treated lumber, which would at least stop the exterior of the beds disintegrating as quickly?
Sure, using pond liner will prevent the copper arsenic from getting in your flowers or food crops right away. However as the wood ages the preservatives will wash into the soil adjacent to your bed. Any plants with spreading roots will take up the preservatives.
The savings in cost for using pressure treated wood are not so great that I would take the chance. Average out the extra cost of using a rot resistant wood over the life of the raised bed and it will not be very much extra.