Supplier reliability is a critical issue for manufacturing companies. Delivery delays from suppliers create backlog and firefighting on the shop floors. To avoid disruption and hedge against supplier lead time uncertainty, companies rely on diversification, multi-sourcing, and safety lead times. In multi-sourcing, the buyer might order the same product (raw material) from different suppliers. The design of a robust and cost-efficient purchasing/ordering plan in multi-sourcing is a complex task which has a strong impact on the performance of the company. In this study, we investigate the use of robust optimization for the integrated lot-sizing and supplier selection problem under lead time uncertainty. More specifically, we use polyhedral budgeted uncertainty sets. The resulting model determines the ideal lot sizes to minimize the total costs taking into consideration suppliers’ reliability and prices. To solve this problem, a row and column generation approach is proposed. To alleviate scalability issues, we enhance the row and column generation through a robust counterpart formulation, and we propose an efficient fix-and-optimize approach. Our extensive computational experiments show that the fix-and-optimize approach yields good quality solutions within a reasonable amount of computational time. We provide insights into supplier diversification based on the risk profile of the decision-maker. One of the conclusions is that an extremely risk-averse decision-maker selects a single supplier, namely the most reliable one even if it does not offer the lowest price.