For the recently discovered cuprate superconductor Ba 2 CuO 3+δ , we propose a lattice structure which resembles the model considered by Lieb to represent the vastly oxygen-deficient material. We first investigate the stability of the Lieb-lattice structure and then construct a multiorbital Hubbard model based on first-principles calculation. By applying the fluctuation-exchange approximation to the model and solving the linearized Eliashberg equation, we show that s-wave and d-wave pairings closely compete with each other and, more interestingly, that the intraorbital and interorbital pairings coexist. We further show that if the energy of the d 3z 2 −r 2 band is raised to make it "incipient" with the lower edge of the band close to the Fermi level within a realistic band filling regime, s±-wave superconductivity is strongly enhanced. We reveal an intriguing relation between the Lieb model and the two-orbital model for the usual K 2 NiF 4 structure where a close competition between sand d-wave pairings is known to occur. The enhanced superconductivity in the present model is further shown to be related to an enhancement found previously in the bilayer Hubbard model with an incipient band.