Two-phase multiple mapping conditioning / large eddy simulation (MMC-LES) is applied for the first time to lifted spray flames on a vitiated coflow burner. Three flames with different inlet fuel mass loading are investigated. MMC-LES uses a hybrid Eulerian-Lagrangian-Lagrangian approach for the evolution of gas-phase flow, stochastic particles, and liquid fuel droplets, respectively. Due to the benefits of localizing mixing in a reference mixture fraction space, a sparse-Lagrangian distribution of particles is able to be used, permitting computationally efficient simulations of the flame series using gas-phase chemical kinetics that includes 32 species and 167 reactions. Heat and mass transfer between the stochastic particles and evaporative fuel droplets are also local in the reference mixture fraction space. Analysis of the gas-phase temperature fields reveals two distinct flame base stabilization phenomena. The first, which is observed for the low and intermediate fuel loading cases, produces a flat flame base spreading across the central region of the jet. The second, observed for the highest fuel loading case, produces an annular flame base in the shear layer that surrounds a cold central jet region, which is characteristic of autoignition due to entrainment of hot oxidizer from the co-flow. Except for a few axial locations, predicted radial profiles of temperature and liquid-phase velocity/size statistics yield a reasonable agreement with experimental measurements for all three flames. Furthermore, the trend of decreasing lift-off height with an increase in fuel loading is captured well.