Plants provide the basic model for how this can work. Set in place a process that uses the sun's energy to transform local resources into digestible nutrients. Set in place a kind of pollination process that outsources the work usually expended on mating to other organisms. Labor problem: solved. Nothing about these processes necessarily depends on the organism being simple or stationary. We can already do most of this with machines and medicine, though we can't do it as efficiently as plants. Yet.
Intuitively, a lot of these solutions would eventually seem to demand significant lifestyle trade-offs. To take a simple example, humans generally seem to enjoy their courtship rituals, but courtship is intimately bound up with mating, which takes work. Humans also seem to enjoy eating elaborate foods, but it's probably a far more difficult problem to transform abundant resources into elaborate food than it is to transform abundant resources into basic nutrient slurry. Humans generally enjoy moving around, though it's easier to provide sustenance for an organism that stays in one place. And so on.
This all suggests, to me, three points.
First, contrary to the "no free lunch" conventional wisdom of modern economics, there does not seem to be any physical or biological principles that necessarily prevent humans from getting what would essentially amount to a free lunch. Draw from resources as large as the sun and lean on processes as efficient as photosynthesis and the costs of lunch become extraordinarily infinitesimal. I can't think of any objections to this that don't amount to arbitrary anthropocentrism.
Second, the sort of economy/ecology that could facilitate this demands a level of technology we haven't reached yet - but it isn't completely out of sight. The primary challenge is learning to chemically transform abundant elements into complex proteins; we can already do something like this, but only with relatively scarce elements, and quite inefficiently. The secondary challenge would be to facilitate large scale artificial fertilization in a way that maintains a viable population without encountering the moral problem of eugenics.
Third, the sorts of problems we'll encounter at this stage of technological evolution will be qualitatively different than the ones we experience today. Right now the standard trade-off is between leisure and abundance. In the future we will have the option of trading off leisure for things like courtship, or sensory indulgence, or mobility, or even biological autonomy. These seem to suggest some pretty dystopian possibilities, but it's worth bearing in mind that these are all options. They are in any case options that capitalism, grounded as it is in a certain technological economy, cannot provide.