To claim a refund on exports made under LUT (Letter of Undertaking) without paying IGST (Integrated Goods and Services Tax), you need to follow the procedure outlined by the GST authorities. This typically involves filing the necessary documents and forms, such as the shipping bill, export invoice, and relevant declarations, with the GST department. The refund can be claimed through the GST portal by providing the required details and supporting documents. It is advisable to consult with a tax professional or refer to the official GST guidelines for specific instructions on claiming the refund.