An Er:Yb:Lu2Si2O7 microchip laser was constructed by placing a 1.2 mm thick, Y-cut Er:Yb:Lu2Si2O7 microchip between two 1.2 mm thick sapphire crystals, in which input and output mirrors were directly deposited onto one face of each crystal. End-pumped by a continuous-wave 975.4 nm diode laser, a 1564 nm multi-longitudinal-mode laser with a maximum output power of 940 mW and slope efficiency of 20% was realized at an absorbed pump power of 5.5 W when the transmission of output mirror was 2.2%. When the transmission of the output mirror was increased to 6%, a 1537 nm single-longitudinal-mode laser with a maximum output power of 440 mW and slope efficiency of 12% was realized at an absorbed pump power of 4.3 W. The results indicate that the Er:Yb:Lu2Si2O7 crystal is a promising microchip gain medium to realize a single-longitudinal-mode laser.