Water pollution by heavy metals is of increasing concern due to its devastating effects on the environment and on human health. For the removal of heavy metals from water sources, natural materials, such as spent-coffee-grains or orange/banana/chestnut peels, appear to offer a potential cheap alternative to more sophisticated and costly technologies currently in use. However, in order to employ them effectively, it is necessary to gain a deeper understanding - at the molecular level - of the heavy metals-bioorganic-water system and exploit the power of computer simulations. As a step in this direction, we investigate via atomistic simulations the capture of lead ions from water by hemicellulose - the latter being representative of the polysaccharides that are common components of vegetables and fruit peels - as well as the reverse process. A series of independent molecular dynamics simulations, both classical and ab initio, reveals a coherent scenario which is consistent with what one would expect of an efficient capture, i.e. that it be fast and irreversible: (i) binding of the metal ions via adsorption is found to happen spontaneously on both carboxylate and hydroxide functional groups; (ii) in contrast, metal ion desorption, leading to solvation in water, involves sizable free-energy barriers.