In this letter, we propose a lattice reduction (LR) aided joint precoding design for MIMO-relay broadcast communication with the average bit error rate (BER) criterion. We jointly design the signal process flow at both the base station (BS), and the relay station (RS), using the reduced basis of two-stage channel matrices. We further modify the basic precoding design with a novel shift method and a modulo method to improve the power efficiency at the BS and the RS respectively. In addition, the MMSE-SIC algorithm is employed to improve the performance of precoding. Simulations show that, the proposed schemes achieve higher diversity order than the traditional precoding without LR, and the modified schemes significantly outperform the basic design, proving the effectiveness of the proposed methods.