Ex-utero regulation of the lungs' responses to breathing air and continued alveolar development shape adult respiratory health. Applying single-cell transposome hypersensitive site sequencing (scTHS-seq) to over 80,000 cells, we assembled the first regulatory atlas of postnatal human and mouse lung alveolar development. We defined regulatory modules and elucidated new mechanistic insights directing alveolar septation, including alveolar type 1 and myofibroblast cell signaling and differentiation, and a unique human matrix fibroblast population. Incorporating GWAS, we mapped lung function causal variants to myofibroblasts and identified a pathogenic regulatory unit linked to lineage marker FGF18, demonstrating the utility of chromatin accessibility data to uncover disease mechanism targets. Our regulatory map and analysis model provide valuable new resources to investigate age-dependent and species-specific control of critical developmental processes. Furthermore, these resources complement existing atlas efforts to advance our understanding of lung health and disease across the human lifespan.