A new computational method is developed for calculating 2H NMR lineshapes of H2O in microheterogeneous systems, such as lyotropic liquid crystals that exhibit curved lipid/water interfaces. The method presented is based on the stochastic Liouville equation (SLE) in its Langevin form. This means that the Liouville equation of motion is combined with Brownian dynamics simulations to describe the stochastic spin-lattice Liouvillian. The NMR relaxation is caused by translational diffusion of the heavy water molecules, along the curved 2H2O/lipid interface. The model used is a nodal surface approximation of the cubic symmetric gyroid minimal surface. This unit cell is then isotropically expanded or distorted in two dimension. The changes in 2H20 NMR lineshapes have been calculated for the enlarged or the distorted cubic unit cell. The timescale of the residual quadrupole interaction, which determines the NMR lineshape, ranges from the Redfield regime to the slow-motional regime depending on the curvature of the interface. The distortion of the cubic phase illustrates the possibility to explore the intermediate interfaces of a phase transition, by means of 2H2O lineshape analysis.