Physical-layer network coding (PNC) is a communications paradigm that exploits overlapped transmissions to boost the throughput of wireless relay networks. A high point of PNC research was a theoretical proof that PNC that makes use of lattice codes could approach the information-theoretic capacity of a two-way relay network (TWRN), where two end nodes communicate via a relay node. The capacity cannot be achieved by conventional methods of time-division or straightforward network coding. Many practical challenges, however, remain to be addressed before the full potential of lattice-coded PNC can be realized. Two major challenges are: for good performance in lattice-coded PNC, channels of simultaneously transmitting nodes must be aligned; for lattice-coded PNC to be practical, the complexity of lattice encoding at the transmitters and lattice decoding at the receiver must be reduced. We address these challenges and implement a first lattice-coded PNC system on a software-defined radio platform. Specifically, we design and implement a low-overhead channel precoding system that accurately aligns the channels of distributed nodes. In our implementation, the nodes only use low-cost temperature-compensated oscillators---a consequent challenge is that the channel alignment must be done more frequently and more accurately compared with the use of expensive oscillators. The low overhead and accurate channel alignment are achieved by (1)a channel precoding system implemented over FPGA to realize fast feedback of channel state information; (2)a highly-accurate carrier frequency offset estimation method; and (3)a partial-feedback channel estimation method that significantly reduces the feedback information from the receiver to the transmitters for channel precoding at the transmitters. To reduce lattice encoding and decoding complexities, we adapt the low-density lattice code for use in PNC systems.