Multi-item lot-sizing problems faced in industrial contexts are often too large to be directly solved by standard optimization solvers. To this purpose, parallelization approaches are very useful to transform the single resolution of a complex problem into the resolution of smaller independent sub-problems, leading to much smaller computational times. We first motivate and propose new practically relevant instances for the Capacitated Lot-Sizing Problem (CLSP) with lost sales, setup times and target ending inventory. Two ways of paralleli-zing the problem are then introduced. A first approach is based on a Lagrangian relaxation of the item binding capacity constraints. We show that the problem linked to each item can be solved in polynomial time. A second approach uses a parallelized version of Relax-And-Fix and Fix-and-Optimize heuristics where, instead of optimizing the time intervals in chronological order at each iteration, different time intervals are optimized in parallel. The best interval is picked according to various strategies and is fixed for the following iterations.