A macroscopically oriented double diamond inverse bicontinuous cubic phase (QII(D)) of the lipid glycerol monooleate is reversibly converted into a gyroid phase (QII(G)). The initial QII(D) phase is prepared in the form of a film coating the inside of a capillary, deposited under flow, which produces a sample uniaxially oriented with a ⟨110⟩ axis parallel to the symmetry axis of the sample. A transformation is induced by replacing the water within the capillary tube with a solution of poly(ethylene glycol), which draws water out of the QII(D) sample by osmotic stress. This converts the QII(D) phase into a QII(G) phase with two coexisting orientations, with the ⟨100⟩ and ⟨111⟩ axes parallel to the symmetry axis, as demonstrated by small-angle X-ray scattering. The process can then be reversed, to recover the initial orientation of QII(D) phase. The epitaxial relation between the two oriented mesophases is consistent with topology-preserving geometric pathways that have previously been hypothesized for the transformation. Furthermore, this has implications for the production of macroscopically oriented QII(G) phases, in particular with applications as nanomaterial templates.