This paper investigates a two-product dynamic lot-size problem under joint production and lost sales, and analyzes forecast and decision horizons for time-varying costs. We formulate a cost minimization model including the joint setup costs, individual setup costs, variable costs, holding costs and lost sale costs over a finite horizon of T periods. Based on some properties of the optimal solution, we develop an efficient forward dynamic programming algorithm to solve the problem. Based on the monotonicity of the production point and production set for both products, a sufficient condition for obtaining forecast horizon and decision horizon is given through a numerical example, the details of computing the forecast horizon is analyzed, which shows the effectiveness of the proposed model.