Membrane lungs consist of thousands of hollow fiber membranes packed together as a bundle. The devices often suffer from complications because of non-uniform flow through the membrane bundle, including regions of both excessively high flow and stagnant flow. Here, we present a proof-of-concept design for a membrane lung containing a membrane module based on triply periodic minimal surfaces (TPMS). By warping the original TPMS geometries, the local permeability within any region of the module could be raised or lowered, allowing for the tailoring of the blood flow distribution through the device. By creating an iterative optimization scheme for determining the distribution of streamwise permeability inside a computational porous domain, the desired form of a lattice of TPMS elements was determined via simulation. This desired form was translated into a computer-aided design (CAD) model for a prototype device. The device was then produced via additive manufacturing in order to test the novel design against an industry-standard predicate device. Flow distribution was verifiably homogenized and residence time reduced, promising a more efficient performance and increased resistance to thrombosis. This work shows the promising extent to which TPMS can serve as a new building block for exchange processes in medical devices.