Crystallization from oriented hexagonal-packed cylinder (hex) and gyroid (gyr) melt phases in an asymmetric poly(ethylene oxide)-b-poly(isoprene) diblock copolymer is investigated by small-angle X-ray scattering with simultaneous rheology. Crystallization from a shear-oriented hex phase leads to crystalline lamellar planes parallel to the cylinders and a step increase in domain spacing. Crystallization from an oriented gyroid crystal, grown from a shear-aligned hex phase, is templated by the {220} lattice planes, leading to an oriented crystalline lamellar phase. The domain spacing increases by 40% on crystallization, indicating a transition that is strictly not epitaxial, although crystallographic register between lattice planes is maintained. The orientation of the lamellar crystal structure is compared to that recently observed for a poly(oxybutylene)-b-poly(oxyethylene) diblock crystallized from an aligned gyroid phase.