Lot-order assignment is the process of assigning items in lots being processed in a production facility to orders to meet due-dates of the orders. In this study, we consider the lot-order assignment problem (LOAP) with the objective of minimizing total tardiness of the orders with distinct due dates. We address similarity relationships between the LOAP and the single machine total tardiness scheduling problem (SMTTSP) and suggest priority rules for the LOAP based on those for the SMTTSP. Performances of the priority rules are compared with each other and with that of the commercial optimization software package in computational experiments.