LnBaCo2O5+δ (Ln = La, Pr, Nd, Sm, Gd, and Y) was synthesized via an EDTA–citrate complexing process. The particular Ln3+ dopant had a significant effect on the oxide’s phase structure/stability, oxygen content, electrical conductivity, oxygen permeability, and cathode performance. Stable, cation-ordered oxides with layered lattice structures were obtained with medium-sized Ln3+ ions over a wide range of oxygen partial pressures, a property essential for applications as oxygen separation membranes and solid oxide fuel cell (SOFC) cathodes. PrBaCo2O5+δ demonstrated the highest oxygen flux (∼5.09 × 10−7 mol cm−2 s−1 at 900 °C), but this value was still significantly lower than that of Ba0.5Sr0.5Co0.8Fe0.2O3−δ perovskite (∼3.1 × 10−6 mol cm−2 s−1 at 900 °C). The observed difference was attributed to the much longer diffusion distance through a polycrystalline membrane with a layered lattice structure than through cubic perovskite because bulk diffusion was the rate-limiting step of permeation. An area-specific resistance of ∼0.213 Ω cm2 was achieved at 600 °C with a PrBaCo2O5+δ cathode, suggesting that the layer-structured oxides were promising alternatives to ceramic membranes for SOFC cathodes.