We study transient drop deformation in dilute emulsions for large values of the capillary number Ca. We consider steady planar linear flows characterized by the dimensionless vorticity β. For drop-to-matrix viscosity ratios λ < 1, we find that the drops are strongly elongated by the extensional component of the flow and widen along the vorticity direction because of the compressional component, thus assuming flat lamellar configurations and leading to remarkable interfacial area generation. We investigate the lamellar morphology using adaptive boundary-integral simulations1,2 and video microscopy.3,4 We find agreement between the experiments and the simulations. The extent of drop widening and interfacial area generation is strongly reduced by a small but finite interfacial tension. Widening occurs only above a minimum capillary number, which increases with the viscosity ratio λ and the vorticity β. The persistence of lamellar configurations is examined. As drops lengthen and flatten, local capillarity associated with high surface curvatures eventually becomes effective, and widening disappears. The development of a lamellar microstructure is thus a transitory phenomenon at finite capillary numbers: flattened drops evolve into slender cylindrical threads of fluid that finally break up.