We report the presence of charge-density waves (CDW's) in the planar square lattices of the layered compounds LaT2-xSbx for 0 less than or equal to x less than or equal to 1, which we have studied through electron microprobe analysis, powder- and single-crystal x-ray diffraction, and transmission electron microscopy. We have identified superlattice reflections with wave vectors spanning large parallel sheets of Fermi surfaces derived from extended-Huckel tight-binding band calculations performed on two-dimensional Te square sheets. As Sb substitutes for Te in LaTe2, the band filling of the square sheets is continuously decreased, with essentially no deviation from the LaTe2 substructure. Through the series, the CDW wave vector follows the changes in the Fermi surface. The CDW's are observed at room temperature and we see no evidence of significant disorder effects with Sb doping. This work establishes LaTe2-xSbx as a family of materials in which the CDW is dependent on Fermi-surface energetics, in contrast to other CDW materials in which lattice strain forces the structural distortion to remain commensurate.