Using density functional theory, we have theoretically studied the formation of neutral lithium-aromatic complexes R-nLi and R-nLi-R, where R is benzene, naphthalene, or pyrene. We first find that the maximum number of lithium atoms n in the complexes increases with the size of R. In addition, pyrene favors the sandwich compound R-4Li-R over R-4Li more than three times that of the corresponding tendency for benzene, strongly suggesting the possible existence of oligomer (R-4Li)(x). We have also investigated energetics and band structures of infinite one-dimensional crystals of R-nLi, finding them metallic. Detailed analysis of the electronic structure shows that all these observations are related to the strong electrostatic interaction among the species, which is originated from the charge transfer from Li atoms to the aromatic rings. In addition, it is shown that the pyrene crystal is mechanically stable with respect to deformation. This also suggests the possibility of its existence, which, in turn, holds potential application in lithium storage in respect to its large Li/C ratio.