LRS Bianchi type-I models have been studied in the cosmological theory based on Lyra's geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for variable deceleration parameter models of the universe. We have compared our models with those of Einstein's field theory with the cosmological term $\Lambda$. Our frame of reference is restricted to the recent Ia observations of supernovae. Some physical behaviour of the models is also examined in the presence of perfect fluids.