This work introduces a Graph Neural Network (GNN)-aided "fix-and-optimize" strategy designed to efficiently reoptimize Lot Sizing Problems (LSP) when facing sudden machine breakdowns. The proposed method leverages a GNN to predict which binary setup variables in the MILP formulation should be fixed, allowing the solver to focus exclusively on optimizing a reduced subset of variables. Since GNNs can handle variable-sized inputs, this approach works on variable-sized LSP instances and different kinds of machine breakdowns. The approach performs significantly better than a standard baseline approach that involves resolving the MILP formulation using a quickly repaired solution as a warm-start.