A normal-metal/insulator/superconductor (NIS) tunnel junction can be applied to cool electrons by biasing the junction suitably with external voltage. Because of the symmetry with bias voltage, two NIS junctions in series can form an efficient microrefrigerator. So far our SINIS microrefrigerator has been capable of reaching electronic temperatures of about 100 mK starting from 300 mK. To achieve appreciable refrigeration of the underlying lattice, microrefrigerator must be thermally decoupled from the bulk substrate. We have demonstrated experimentally the reduction of lattice temperature of a few mK at 200 mK by extending the normal electrode on a thin dielectric membrane. Methods to improve the efficiency of lattice refrigeration are discussed.