  We define a link lattice complex for plumbed links, generalizing
constructions of Ozsv\'ath, Stipsicz and Szab\'o, and of Gorsky and N\'emethi.
We prove that for all plumbed links in rational homology 3-spheres, the link
lattice complex is homotopy equivalent to the link Floer complex as an
$A_\infty$-module. Additionally, we prove that the link Floer complex of a
plumbed L-space link is a free resolution of its homology. As a consequence, we
give an algorithm to compute the link Floer complexes of plumbed L-space links,
in particular of algebraic links, from their multivariable Alexander
polynomial.
