The leaf epidermis is a dynamic biomechanical shell that integrates growth across spatial scales to influence organ morphology. Pavement cells, the fundamental unit of this tissue, morph irreversibly into highly lobed cells that drive planar leaf expansion. Here, we define how tissue-scale cell wall tensile forces and the microtubule-cellulose synthase systems dictate the patterns of interdigitated growth in real time. A morphologically potent subset of cortical microtubules span the periclinal and anticlinal cell faces to pattern cellulose fibres that generate a patch of anisotropic wall. The subsequent local polarized growth is mechanically coupled to the adjacent cell via a pectin-rich middle lamella, and this drives lobe formation. Finite element pavement cell models revealed cell wall tensile stress as an upstream patterning element that links cell- and tissue-scale biomechanical parameters to interdigitated growth. Cell lobing in leaves is evolutionarily conserved, occurs in multiple cell types and is associated with important agronomic traits. Our general mechanistic models of lobe formation provide a foundation to analyse the cellular basis of leaf morphology and function.