Plants cells are encaged in a rigid cell wall that preclude cell migration. In consequence, plants rely on oriented cell divisions and anisotropic growth to shape their organs. This mode of growth entails that mechanical constraints between tissue may have an important role in morphogenesis. In Arabidopsis thaliana, lateral roots originate from cells located deep within the main root and have to emerge through several cell layers of the main root. We use light sheet based fluorescence microscopy to non-invasively capture with subcellular resolution the formation of lateral roots. Quantitative analysis and generation of virtual lateral roots from these datasets allow to study with unprecedented details how patterns of cell division, organ growth and overlaying tissues integrate during plant organ morphogenesis. In particular, we observe that although the patterns of division during lateral root formation are not stereotypical, lateral root morphogenesis is underpinned by few invariant principles that govern the establishment of its typical shape and layered organization.