The shape of the lumbar spine influences its function and dysfunction. Yet examining the influence of geometric differences associated with pathology or demographics on lumbar biomechanics is challenging in vivo where these effects cannot be isolated, and the use of simple anatomical measurements does not fully capture the complex three-dimensional geometry. The goal of this work was to develop and share morphable models of the lumbar spine that allow geometry to be varied according to pathology, demographics, or anatomical measurements. Partial least squares regression was used to generate statistical shape models that quantify geometric differences associated with pathology, demographics, and anatomical measurements from the lumbar spines of 87 patients. To determine if the morphable models detected meaningful geometric differences, the ability of the morphable models to classify spines was compared with models generated from random labels. The models for disc herniation (p < 0.04), spondylolisthesis (p < 0.001), and sex (p < 0.01) all performed significantly better than the random models. Age was predicted with a root mean square error of 14.1 years using the age-based model. The morphable models for anatomical measurements were able to produce instances with root mean square errors less than 0.8°, 0.3 cm2, and 0.7 mm between desired and resulting measurements. This method can be used to produce morphable models that enable further analysis of the relationship among shape, pathology, demographics, and function through computational simulations. The morphable models and code are available at https://github.com/aclouthier/morphable-lumbar-model.