The Drosophila external sensory organ forms in a lineage elaborating from a single precursor cell via a stereotypical series of asymmetric divisions. HAMLET transcription factor expression demarcates the lineage branch that generates two internal cell types, the external sensory neuron and thecogen. In HAMLET mutant organs, these internal cells are converted to external cells via an unprecedented cousin-cousin cell-fate respecification event. Conversely, ectopic HAMLET expression in the external cell branch leads to internal cell production. The fate-determining signals NOTCH and PAX2 act at multiple stages of lineage elaboration and HAMLET acts to modulate their activity in a branch-specific manner.