We disclose a precursor-driven order - order transition (OOT) between bcc and fcc lattices in a sphere-forming blend of a poly(ethylene oxide)-block-poly(1,4-butadiene) (PEO-b-PB) and a PB homopolymer (h-PB). The blend as cast from toluene exhibited a metastable trapped fcc (t-fcc) phase, which showed no sign of transformation into bcc phase on heating to 260 degrees C. Annealing the as-cast blend at -20 degrees C disturbed the long-range order of t-fcc due to crystallization of PEO within the spherical microdomains. A significant portion of the rather disorderly arranged crystalline domains relaxed to grains having the equilibrium bcc lattice, when the PEO crystals were melted at elevated temperatures. The bcc grains thus developed then acted as the precursor to induce a transformation of t-fcc phase to bcc phase on heating up to 205 degrees C. Since the t-fcc phase was not completely wiped out through this process, a bcc-to-fcc OOT assisted by the residual t-fcc precursor set in on heating from 205 to 260 degrees C where fcc became the stable packing symmetry. Subsequent cooling from 260 degrees C recovered the bcc phase and the blend cooled to 110 degrees C was essentially fcc free. Because of the absence of fcc grain, the thermodynamically prescribed bcc-to-fcc OOT could no longer take place on reheating. Our results revealed the necessity of bcc or fcc precursor for initiating the relevant OOT and hence implied a high activation barrier associated with the transition. The activation barrier was proposed to be entropic in origin stemming from the deformations of PB blocks and h-PB chains in the lattice transition proceeding through the Bain distortion mechanism.